diff --git a/Doc/library/poplib.rst b/Doc/library/poplib.rst
index e248d6b..deb49fc 100644
--- a/Doc/library/poplib.rst
+++ b/Doc/library/poplib.rst
@@ -53,6 +53,10 @@
    .. versionchanged:: 3.2
       *context* parameter added.
 
+   .. versionchanged:: 3.4
+      The class now supports hostname check with
+      :attr:`SSLContext.check_hostname` and *Server Name Indicator* (see
+      :data:`~ssl.HAS_SNI`).
 
 One exception is defined as an attribute of the :mod:`poplib` module:
 
@@ -198,6 +202,11 @@
 
    .. versionadded:: 3.4
 
+   .. versionchanged:: 3.4
+      The method now supports hostname check with
+      :attr:`SSLContext.check_hostname` and *Server Name Indicator* (see
+      :data:`~ssl.HAS_SNI`).
+
 
 Instances of :class:`POP3_SSL` have no additional methods. The interface of this
 subclass is identical to its parent.
diff --git a/Lib/poplib.py b/Lib/poplib.py
index 00ffbcb..23a3517 100644
--- a/Lib/poplib.py
+++ b/Lib/poplib.py
@@ -387,7 +387,9 @@
         if context is None:
             context = ssl._create_stdlib_context()
         resp = self._shortcmd('STLS')
-        self.sock = context.wrap_socket(self.sock)
+        server_hostname = self.host if ssl.HAS_SNI else None
+        self.sock = context.wrap_socket(self.sock,
+                                        server_hostname=server_hostname)
         self.file = self.sock.makefile('rb')
         self._tls_established = True
         return resp
@@ -428,7 +430,9 @@
 
         def _create_socket(self, timeout):
             sock = POP3._create_socket(self, timeout)
-            sock = self.context.wrap_socket(sock)
+            server_hostname = self.host if ssl.HAS_SNI else None
+            sock = self.context.wrap_socket(sock,
+                                            server_hostname=server_hostname)
             return sock
 
         def stls(self, keyfile=None, certfile=None, context=None):
diff --git a/Lib/test/test_poplib.py b/Lib/test/test_poplib.py
index 70fe426..31f8a3c 100644
--- a/Lib/test/test_poplib.py
+++ b/Lib/test/test_poplib.py
@@ -23,7 +23,8 @@
     import ssl
 
     SUPPORTS_SSL = True
-    CERTFILE = os.path.join(os.path.dirname(__file__) or os.curdir, "keycert.pem")
+    CERTFILE = os.path.join(os.path.dirname(__file__) or os.curdir, "keycert3.pem")
+    CAFILE = os.path.join(os.path.dirname(__file__) or os.curdir, "pycacert.pem")
 requires_ssl = skipUnless(SUPPORTS_SSL, 'SSL not supported')
 
 # the dummy data returned by server when LIST and RETR commands are issued
@@ -332,6 +333,12 @@
     def test_stls_context(self):
         expected = b'+OK Begin TLS negotiation'
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLSv1)
+        ctx.load_verify_locations(CAFILE)
+        ctx.verify_mode = ssl.CERT_REQUIRED
+        ctx.check_hostname = True
+        with self.assertRaises(ssl.CertificateError):
+            resp = self.client.stls(context=ctx)
+        self.client = poplib.POP3("localhost", self.server.port, timeout=3)
         resp = self.client.stls(context=ctx)
         self.assertEqual(resp, expected)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 3785840..9f0dbb9 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -18,6 +18,9 @@
 Library
 -------
 
+- Issue #19784: poplib now supports SSLContext.check_hostname and server name
+  indication for TLS/SSL connections.
+
 - Issue #19782: imaplib now supports SSLContext.check_hostname and server name
   indication for TLS/SSL connections.