diff --git a/Lib/http/client.py b/Lib/http/client.py
index 1039fa5..6c38c4a 100644
--- a/Lib/http/client.py
+++ b/Lib/http/client.py
@@ -1081,7 +1081,9 @@
                 self.sock = sock
                 self._tunnel()
 
-            self.sock = self._context.wrap_socket(sock)
+            server_hostname = self.host if ssl.HAS_SNI else None
+            self.sock = self._context.wrap_socket(sock,
+                                                  server_hostname=server_hostname)
             try:
                 if self._check_hostname:
                     ssl.match_hostname(self.sock.getpeercert(), self.host)
diff --git a/Lib/ssl.py b/Lib/ssl.py
index ae8aaef..f1a0e45 100644
--- a/Lib/ssl.py
+++ b/Lib/ssl.py
@@ -77,6 +77,7 @@
     SSL_ERROR_EOF,
     SSL_ERROR_INVALID_ERROR_CODE,
     )
+from _ssl import HAS_SNI
 
 from socket import getnameinfo as _getnameinfo
 from socket import error as socket_error
@@ -158,10 +159,12 @@
 
     def wrap_socket(self, sock, server_side=False,
                     do_handshake_on_connect=True,
-                    suppress_ragged_eofs=True):
+                    suppress_ragged_eofs=True,
+                    server_hostname=None):
         return SSLSocket(sock=sock, server_side=server_side,
                          do_handshake_on_connect=do_handshake_on_connect,
                          suppress_ragged_eofs=suppress_ragged_eofs,
+                         server_hostname=server_hostname,
                          _context=self)
 
 
@@ -176,6 +179,7 @@
                  do_handshake_on_connect=True,
                  family=AF_INET, type=SOCK_STREAM, proto=0, fileno=None,
                  suppress_ragged_eofs=True, ciphers=None,
+                 server_hostname=None,
                  _context=None):
 
         if _context:
@@ -202,7 +206,11 @@
             self.ssl_version = ssl_version
             self.ca_certs = ca_certs
             self.ciphers = ciphers
+        if server_side and server_hostname:
+            raise ValueError("server_hostname can only be specified "
+                             "in client mode")
         self.server_side = server_side
+        self.server_hostname = server_hostname
         self.do_handshake_on_connect = do_handshake_on_connect
         self.suppress_ragged_eofs = suppress_ragged_eofs
         connected = False
@@ -232,7 +240,8 @@
         if connected:
             # create the SSL object
             try:
-                self._sslobj = self.context._wrap_socket(self, server_side)
+                self._sslobj = self.context._wrap_socket(self, server_side,
+                                                         server_hostname)
                 if do_handshake_on_connect:
                     timeout = self.gettimeout()
                     if timeout == 0.0:
@@ -431,7 +440,7 @@
         if self._sslobj:
             raise ValueError("attempt to connect already-connected SSLSocket!")
         socket.connect(self, addr)
-        self._sslobj = self.context._wrap_socket(self, False)
+        self._sslobj = self.context._wrap_socket(self, False, self.server_hostname)
         try:
             if self.do_handshake_on_connect:
                 self.do_handshake()
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 0c8a8e6..67bc01a 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -89,6 +89,7 @@
         ssl.CERT_NONE
         ssl.CERT_OPTIONAL
         ssl.CERT_REQUIRED
+        self.assertIn(ssl.HAS_SNI, {True, False})
 
     def test_random(self):
         v = ssl.RAND_status()
@@ -277,6 +278,12 @@
         self.assertRaises(ValueError, ssl.match_hostname, None, 'example.com')
         self.assertRaises(ValueError, ssl.match_hostname, {}, 'example.com')
 
+    def test_server_side(self):
+        # server_hostname doesn't work for server sockets
+        ctx = ssl.SSLContext(ssl.PROTOCOL_SSLv23)
+        sock = socket.socket()
+        self.assertRaises(ValueError, ctx.wrap_socket, sock, True,
+                          server_hostname="some.hostname")
 
 class ContextTests(unittest.TestCase):
 
@@ -441,6 +448,14 @@
                 self.assertEqual({}, s.getpeercert())
             finally:
                 s.close()
+            # Same with a server hostname
+            s = ctx.wrap_socket(socket.socket(socket.AF_INET),
+                                server_hostname="svn.python.org")
+            if ssl.HAS_SNI:
+                s.connect(("svn.python.org", 443))
+                s.close()
+            else:
+                self.assertRaises(ValueError, s.connect, ("svn.python.org", 443))
             # This should fail because we have no verification certs
             ctx.verify_mode = ssl.CERT_REQUIRED
             s = ctx.wrap_socket(socket.socket(socket.AF_INET))
@@ -1500,6 +1515,7 @@
         print("test_ssl: testing with %r %r" %
             (ssl.OPENSSL_VERSION, ssl.OPENSSL_VERSION_INFO))
         print("          under %s" % plat)
+        print("          HAS_SNI = %r" % ssl.HAS_SNI)
 
     for filename in [
         CERTFILE, SVN_PYTHON_ORG_ROOT_CERT, BYTES_CERTFILE,
diff --git a/Lib/test/test_urllib2net.py b/Lib/test/test_urllib2net.py
index a4af01a..0a777c4 100644
--- a/Lib/test/test_urllib2net.py
+++ b/Lib/test/test_urllib2net.py
@@ -9,6 +9,10 @@
 import urllib.error
 import urllib.request
 import sys
+try:
+    import ssl
+except ImportError:
+    ssl = None
 
 TIMEOUT = 60  # seconds
 
@@ -278,13 +282,34 @@
         self.assertEqual(u.fp.fp.raw._sock.gettimeout(), 60)
 
 
+@unittest.skipUnless(ssl, "requires SSL support")
+class HTTPSTests(unittest.TestCase):
+
+    def test_sni(self):
+        # Checks that Server Name Indication works, if supported by the
+        # OpenSSL linked to.
+        # The ssl module itself doesn't have server-side support for SNI,
+        # so we rely on a third-party test site.
+        expect_sni = ssl.HAS_SNI
+        with support.transient_internet("bob.sni.velox.ch"):
+            u = urllib.request.urlopen("https://bob.sni.velox.ch/")
+            contents = u.readall()
+            if expect_sni:
+                self.assertIn(b"Great", contents)
+                self.assertNotIn(b"Unfortunately", contents)
+            else:
+                self.assertNotIn(b"Great", contents)
+                self.assertIn(b"Unfortunately", contents)
+
+
 def test_main():
     support.requires("network")
     support.run_unittest(AuthTests,
-                              OtherNetworkTests,
-                              CloseSocketTest,
-                              TimeoutTest,
-                              )
+                         HTTPSTests,
+                         OtherNetworkTests,
+                         CloseSocketTest,
+                         TimeoutTest,
+                         )
 
 if __name__ == "__main__":
     test_main()