diff --git a/Doc/library/zipfile.rst b/Doc/library/zipfile.rst
index 493e172..409de44 100644
--- a/Doc/library/zipfile.rst
+++ b/Doc/library/zipfile.rst
@@ -97,12 +97,20 @@
 
    .. versionadded:: 3.3
 
+.. data:: ZIP_LZMA
+
+   The numeric constant for the LZMA compression method.  This requires the
+   lzma module.
+
+   .. versionadded:: 3.3
+
    .. note::
 
       The ZIP file format specification has included support for bzip2 compression
-      since 2001. However, some tools (including older Python releases) do not
-      support it, and may either refuse to process the ZIP file altogether, or
-      fail to extract individual files.
+      since 2001, and for LZMA compression since 2006. However, some tools
+      (including older Python releases) do not support these compression
+      methods, and may either refuse to process the ZIP file altogether,
+      or fail to extract individual files.
 
 
 .. seealso::
@@ -133,11 +141,11 @@
    adding a ZIP archive to another file (such as :file:`python.exe`).  If
    *mode* is ``a`` and the file does not exist at all, it is created.
    *compression* is the ZIP compression method to use when writing the archive,
-   and should be :const:`ZIP_STORED`, :const:`ZIP_DEFLATED`; or
-   :const:`ZIP_DEFLATED`; unrecognized
-   values will cause :exc:`RuntimeError` to be raised.  If :const:`ZIP_DEFLATED` or
-   :const:`ZIP_BZIP2` is specified but the corresponded module
-   (:mod:`zlib` or :mod:`bz2`) is not available, :exc:`RuntimeError`
+   and should be :const:`ZIP_STORED`, :const:`ZIP_DEFLATED`,
+   :const:`ZIP_BZIP2` or :const:`ZIP_LZMA`; unrecognized
+   values will cause :exc:`RuntimeError` to be raised.  If :const:`ZIP_DEFLATED`,
+   :const:`ZIP_BZIP2` or :const:`ZIP_LZMA` is specified but the corresponded module
+   (:mod:`zlib`, :mod:`bz2` or :mod:`lzma`) is not available, :exc:`RuntimeError`
    is also raised. The default is :const:`ZIP_STORED`.  If *allowZip64* is
    ``True`` zipfile will create ZIP files that use the ZIP64 extensions when
    the zipfile is larger than 2 GB. If it is  false (the default) :mod:`zipfile`
@@ -161,7 +169,7 @@
       Added the ability to use :class:`ZipFile` as a context manager.
 
    .. versionchanged:: 3.3
-      Added support for :mod:`bzip2` compression.
+      Added support for :mod:`bzip2` and :mod:`lzma` compression.
 
 
 .. method:: ZipFile.close()
diff --git a/Lib/test/support.py b/Lib/test/support.py
index c92fa00..4568e54 100644
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -45,6 +45,11 @@
 except ImportError:
     bz2 = None
 
+try:
+    import lzma
+except ImportError:
+    lzma = None
+
 __all__ = [
     "Error", "TestFailed", "ResourceDenied", "import_module",
     "verbose", "use_resources", "max_memuse", "record_original_stdout",
@@ -62,7 +67,7 @@
     "get_attribute", "swap_item", "swap_attr", "requires_IEEE_754",
     "TestHandler", "Matcher", "can_symlink", "skip_unless_symlink",
     "import_fresh_module", "requires_zlib", "PIPE_MAX_SIZE", "failfast",
-    "anticipate_failure", "run_with_tz", "requires_bz2"
+    "anticipate_failure", "run_with_tz", "requires_bz2", "requires_lzma"
     ]
 
 class Error(Exception):
@@ -513,6 +518,8 @@
 
 requires_bz2 = unittest.skipUnless(bz2, 'requires bz2')
 
+requires_lzma = unittest.skipUnless(lzma, 'requires lzma')
+
 is_jython = sys.platform.startswith('java')
 
 # Filename used for testing
diff --git a/Lib/test/test_zipfile.py b/Lib/test/test_zipfile.py
index 80d45f5..0772236 100644
--- a/Lib/test/test_zipfile.py
+++ b/Lib/test/test_zipfile.py
@@ -13,7 +13,7 @@
 from random import randint, random
 from unittest import skipUnless
 
-from test.support import TESTFN, run_unittest, findfile, unlink, requires_zlib, requires_bz2
+from test.support import TESTFN, run_unittest, findfile, unlink, requires_zlib, requires_bz2, requires_lzma
 
 TESTFN2 = TESTFN + "2"
 TESTFNDIR = TESTFN + "d"
@@ -361,6 +361,55 @@
                 self.assertEqual(openobj.read(1), b'1')
                 self.assertEqual(openobj.read(1), b'2')
 
+    @requires_lzma
+    def test_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_open_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_open_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_random_open_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_random_open_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readline_read_lzma(self):
+        # Issue #7610: calls to readline() interleaved with calls to read().
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_readline_read_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readline_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_readline_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readlines_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_readlines_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_iterlines_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_iterlines_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_low_compression_lzma(self):
+        """Check for cases where compressed data is larger than original."""
+        # Create the ZIP archive
+        with zipfile.ZipFile(TESTFN2, "w", zipfile.ZIP_LZMA) as zipfp:
+            zipfp.writestr("strfile", '12')
+
+        # Get an open object for strfile
+        with zipfile.ZipFile(TESTFN2, "r", zipfile.ZIP_LZMA) as zipfp:
+            with zipfp.open("strfile") as openobj:
+                self.assertEqual(openobj.read(1), b'1')
+                self.assertEqual(openobj.read(1), b'2')
+
     def test_absolute_arcnames(self):
         with zipfile.ZipFile(TESTFN2, "w", zipfile.ZIP_STORED) as zipfp:
             zipfp.write(TESTFN, "/absolute")
@@ -508,6 +557,13 @@
         info = zipfp.getinfo('b.txt')
         self.assertEqual(info.compress_type, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_writestr_compression_lzma(self):
+        zipfp = zipfile.ZipFile(TESTFN2, "w")
+        zipfp.writestr("b.txt", "hello world", compress_type=zipfile.ZIP_LZMA)
+        info = zipfp.getinfo('b.txt')
+        self.assertEqual(info.compress_type, zipfile.ZIP_LZMA)
+
     def zip_test_writestr_permissions(self, f, compression):
         # Make sure that writestr creates files with mode 0600,
         # when it is passed a name rather than a ZipInfo instance.
@@ -686,6 +742,11 @@
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
             self.zip_test(f, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_test(f, zipfile.ZIP_LZMA)
+
     def test_absolute_arcnames(self):
         with zipfile.ZipFile(TESTFN2, "w", zipfile.ZIP_STORED,
                              allowZip64=True) as zipfp:
@@ -826,6 +887,16 @@
             b'\x00 \x80\x80\x81\x00\x00\x00\x00afilePK'
             b'\x05\x06\x00\x00\x00\x00\x01\x00\x01\x003\x00\x00\x00[\x00'
             b'\x00\x00\x00\x00'),
+        zipfile.ZIP_LZMA: (
+            b'PK\x03\x04\x14\x03\x00\x00\x0e\x00nu\x0c=FA'
+            b'KE\x1b\x00\x00\x00n\x00\x00\x00\x05\x00\x00\x00af'
+            b'ile\t\x04\x05\x00]\x00\x00\x00\x04\x004\x19I'
+            b'\xee\x8d\xe9\x17\x89:3`\tq!.8\x00PK'
+            b'\x01\x02\x14\x03\x14\x03\x00\x00\x0e\x00nu\x0c=FA'
+            b'KE\x1b\x00\x00\x00n\x00\x00\x00\x05\x00\x00\x00\x00\x00'
+            b'\x00\x00\x00\x00 \x80\x80\x81\x00\x00\x00\x00afil'
+            b'ePK\x05\x06\x00\x00\x00\x00\x01\x00\x01\x003\x00\x00'
+            b'\x00>\x00\x00\x00\x00\x00'),
     }
 
     def test_unsupported_version(self):
@@ -1104,6 +1175,10 @@
     def test_testzip_with_bad_crc_bzip2(self):
         self.check_testzip_with_bad_crc(zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_testzip_with_bad_crc_lzma(self):
+        self.check_testzip_with_bad_crc(zipfile.ZIP_LZMA)
+
     def check_read_with_bad_crc(self, compression):
         """Tests that files with bad CRCs raise a BadZipFile exception when read."""
         zipdata = self.zips_with_bad_crc[compression]
@@ -1136,6 +1211,10 @@
     def test_read_with_bad_crc_bzip2(self):
         self.check_read_with_bad_crc(zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_read_with_bad_crc_lzma(self):
+        self.check_read_with_bad_crc(zipfile.ZIP_LZMA)
+
     def check_read_return_size(self, compression):
         # Issue #9837: ZipExtFile.read() shouldn't return more bytes
         # than requested.
@@ -1160,6 +1239,10 @@
     def test_read_return_size_bzip2(self):
         self.check_read_return_size(zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_read_return_size_lzma(self):
+        self.check_read_return_size(zipfile.ZIP_LZMA)
+
     def test_empty_zipfile(self):
         # Check that creating a file in 'w' or 'a' mode and closing without
         # adding any files to the archives creates a valid empty ZIP file
@@ -1306,6 +1389,11 @@
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
             self.zip_test(f, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_test(f, zipfile.ZIP_LZMA)
+
     def zip_open_test(self, f, compression):
         self.make_test_archive(f, compression)
 
@@ -1351,6 +1439,11 @@
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
             self.zip_open_test(f, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_open_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_open_test(f, zipfile.ZIP_LZMA)
+
     def zip_random_open_test(self, f, compression):
         self.make_test_archive(f, compression)
 
@@ -1384,6 +1477,11 @@
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
             self.zip_random_open_test(f, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_random_open_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.zip_random_open_test(f, zipfile.ZIP_LZMA)
+
 
 @requires_zlib
 class TestsWithMultipleOpens(unittest.TestCase):
@@ -1628,6 +1726,31 @@
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
             self.iterlines_test(f, zipfile.ZIP_BZIP2)
 
+    @requires_lzma
+    def test_read_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.read_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readline_read_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.readline_read_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readline_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.readline_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_readlines_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.readlines_test(f, zipfile.ZIP_LZMA)
+
+    @requires_lzma
+    def test_iterlines_lzma(self):
+        for f in (TESTFN2, TemporaryFile(), io.BytesIO()):
+            self.iterlines_test(f, zipfile.ZIP_LZMA)
+
     def tearDown(self):
         for sep, fn in self.arcfiles.items():
             os.remove(fn)
diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index c53b127..c127c2c 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -27,8 +27,13 @@
 except ImportError:
     bz2 = None
 
+try:
+    import lzma # We may need its compression method
+except ImportError:
+    lzma = None
+
 __all__ = ["BadZipFile", "BadZipfile", "error",
-           "ZIP_STORED", "ZIP_DEFLATED", "ZIP_BZIP2",
+           "ZIP_STORED", "ZIP_DEFLATED", "ZIP_BZIP2", "ZIP_LZMA",
            "is_zipfile", "ZipInfo", "ZipFile", "PyZipFile", "LargeZipFile"]
 
 class BadZipFile(Exception):
@@ -52,13 +57,15 @@
 ZIP_STORED = 0
 ZIP_DEFLATED = 8
 ZIP_BZIP2 = 12
+ZIP_LZMA = 14
 # Other ZIP compression methods not supported
 
 DEFAULT_VERSION = 20
 ZIP64_VERSION = 45
 BZIP2_VERSION = 46
+LZMA_VERSION = 63
 # we recognize (but not necessarily support) all features up to that version
-MAX_EXTRACT_VERSION = 46
+MAX_EXTRACT_VERSION = 63
 
 # Below are some formats and associated data for reading/writing headers using
 # the struct module.  The names and structures of headers/records are those used
@@ -367,6 +374,8 @@
 
         if self.compress_type == ZIP_BZIP2:
             min_version = max(BZIP2_VERSION, min_version)
+        elif self.compress_type == ZIP_LZMA:
+            min_version = max(LZMA_VERSION, min_version)
 
         self.extract_version = max(min_version, self.extract_version)
         self.create_version = max(min_version, self.create_version)
@@ -480,6 +489,77 @@
         return c
 
 
+class LZMACompressor:
+
+    def __init__(self):
+        self._comp = None
+
+    def _init(self):
+        props = lzma.encode_filter_properties({'id': lzma.FILTER_LZMA1})
+        self._comp = lzma.LZMACompressor(lzma.FORMAT_RAW, filters=[
+                lzma.decode_filter_properties(lzma.FILTER_LZMA1, props)
+        ])
+        return struct.pack('<BBH', 9, 4, len(props)) + props
+
+    def compress(self, data):
+        if self._comp is None:
+            return self._init() + self._comp.compress(data)
+        return self._comp.compress(data)
+
+    def flush(self):
+        if self._comp is None:
+            return self._init() + self._comp.flush()
+        return self._comp.flush()
+
+
+class LZMADecompressor:
+
+    def __init__(self):
+        self._decomp = None
+        self._unconsumed = b''
+        self.eof = False
+
+    def decompress(self, data):
+        if self._decomp is None:
+            self._unconsumed += data
+            if len(self._unconsumed) <= 4:
+                return b''
+            psize, = struct.unpack('<H', self._unconsumed[2:4])
+            if len(self._unconsumed) <= 4 + psize:
+                return b''
+
+            self._decomp = lzma.LZMADecompressor(lzma.FORMAT_RAW, filters=[
+                    lzma.decode_filter_properties(lzma.FILTER_LZMA1,
+                            self._unconsumed[4:4 + psize])
+            ])
+            data = self._unconsumed[4 + psize:]
+            del self._unconsumed
+
+        result = self._decomp.decompress(data)
+        self.eof = self._decomp.eof
+        return result
+
+
+compressor_names = {
+    0: 'store',
+    1: 'shrink',
+    2: 'reduce',
+    3: 'reduce',
+    4: 'reduce',
+    5: 'reduce',
+    6: 'implode',
+    7: 'tokenize',
+    8: 'deflate',
+    9: 'deflate64',
+    10: 'implode',
+    12: 'bzip2',
+    14: 'lzma',
+    18: 'terse',
+    19: 'lz77',
+    97: 'wavpack',
+    98: 'ppmd',
+}
+
 def _check_compression(compression):
     if compression == ZIP_STORED:
         pass
@@ -491,6 +571,10 @@
         if not bz2:
             raise RuntimeError(
                     "Compression requires the (missing) bz2 module")
+    elif compression == ZIP_LZMA:
+        if not lzma:
+            raise RuntimeError(
+                    "Compression requires the (missing) lzma module")
     else:
         raise RuntimeError("That compression method is not supported")
 
@@ -501,6 +585,8 @@
              zlib.DEFLATED, -15)
     elif compress_type == ZIP_BZIP2:
         return bz2.BZ2Compressor()
+    elif compress_type == ZIP_LZMA:
+        return LZMACompressor()
     else:
         return None
 
@@ -512,19 +598,10 @@
         return zlib.decompressobj(-15)
     elif compress_type == ZIP_BZIP2:
         return bz2.BZ2Decompressor()
+    elif compress_type == ZIP_LZMA:
+        return LZMADecompressor()
     else:
-        unknown_compressors = {
-            1: 'shrink',
-            2: 'reduce',
-            3: 'reduce',
-            4: 'reduce',
-            5: 'reduce',
-            6: 'implode',
-            9: 'enhanced deflate',
-            10: 'implode',
-            14: 'lzma',
-            }
-        descr = unknown_compressors.get(compress_type)
+        descr = compressor_names.get(compress_type)
         if descr:
             raise NotImplementedError("compression type %d (%s)" % (compress_type, descr))
         else:
@@ -781,8 +858,8 @@
     file: Either the path to the file, or a file-like object.
           If it is a path, the file will be opened and closed by ZipFile.
     mode: The mode can be either read "r", write "w" or append "a".
-    compression: ZIP_STORED (no compression), ZIP_DEFLATED (requires zlib) or
-                 ZIP_BZIP2 (requires bz2).
+    compression: ZIP_STORED (no compression), ZIP_DEFLATED (requires zlib),
+                 ZIP_BZIP2 (requires bz2) or ZIP_LZMA (requires lzma).
     allowZip64: if True ZipFile will create files with ZIP64 extensions when
                 needed, otherwise it will raise an exception when this would
                 be necessary.
@@ -1062,6 +1139,10 @@
             # Zip 2.7: compressed patched data
             raise NotImplementedError("compressed patched data (flag bit 5)")
 
+        if zinfo.flag_bits & 0x40:
+            # strong encryption
+            raise NotImplementedError("strong encryption (flag bit 6)")
+
         if zinfo.flag_bits & 0x800:
             # UTF-8 filename
             fname_str = fname.decode("utf-8")
@@ -1220,6 +1301,9 @@
         zinfo.file_size = st.st_size
         zinfo.flag_bits = 0x00
         zinfo.header_offset = self.fp.tell()    # Start of header bytes
+        if zinfo.compress_type == ZIP_LZMA:
+            # Compressed data includes an end-of-stream (EOS) marker
+            zinfo.flag_bits |= 0x02
 
         self._writecheck(zinfo)
         self._didModify = True
@@ -1292,6 +1376,9 @@
         zinfo.header_offset = self.fp.tell()    # Start of header data
         if compress_type is not None:
             zinfo.compress_type = compress_type
+        if zinfo.compress_type == ZIP_LZMA:
+            # Compressed data includes an end-of-stream (EOS) marker
+            zinfo.flag_bits |= 0x02
 
         self._writecheck(zinfo)
         self._didModify = True
@@ -1360,6 +1447,8 @@
 
                 if zinfo.compress_type == ZIP_BZIP2:
                     min_version = max(BZIP2_VERSION, min_version)
+                elif zinfo.compress_type == ZIP_LZMA:
+                    min_version = max(LZMA_VERSION, min_version)
 
                 extract_version = max(min_version, zinfo.extract_version)
                 create_version = max(min_version, zinfo.create_version)
diff --git a/Misc/NEWS b/Misc/NEWS
index a7d1b44..c0f33cb 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -23,6 +23,9 @@
 Library
 -------
 
+- Issue #14366: Support lzma compression in zip files.
+  Patch by Serhiy Storchaka.
+
 - Issue #13959: Introduce importlib.find_loader().
 
 - Issue #14082: shutil.copy2() now copies extended attributes, if possible.