diff --git a/notebook/notebookapp.py b/notebook/notebookapp.py
index 6607dc1a3..8a1bfb248 100755
--- a/notebook/notebookapp.py
+++ b/notebook/notebookapp.py
@@ -1420,8 +1420,13 @@ class NotebookApp(JupyterApp):
         else:
             # SSL may be missing, so only import it if it's to be used
             import ssl
-            # Disable SSLv3 by default, since its use is discouraged.
-            ssl_options.setdefault('ssl_version', ssl.PROTOCOL_TLSv1)
+            # PROTOCOL_TLS selects the highest ssl/tls protocol version that both the client and
+            # server support. When PROTOCOL_TLS is not available use PROTOCOL_SSLv23.
+            # PROTOCOL_TLS is new in version 2.7.13, 3.5.3 and 3.6
+            ssl_options.setdefault(
+                'ssl_version',
+                getattr(ssl, 'PROTOCOL_TLS', ssl.PROTOCOL_SSLv23)
+            )
             if ssl_options.get('ca_certs', False):
                 ssl_options.setdefault('cert_reqs', ssl.CERT_REQUIRED)