diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index a82babb6b9e..367f7d07a41 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -574,7 +574,7 @@ class SSLProtocol(protocols.Protocol):
         # (b'', 1) is a special value in _process_write_backlog() to do
         # the SSL handshake
         self._write_backlog.append((b'', 1))
-        self._loop.call_soon(self._process_write_backlog)
+        self._process_write_backlog()
 
     def _on_handshake_complete(self, handshake_exc):
         self._in_handshake = False
diff --git a/Misc/NEWS.d/next/Library/2018-05-28-22-49-59.bpo-33674.6LFFj7.rst b/Misc/NEWS.d/next/Library/2018-05-28-22-49-59.bpo-33674.6LFFj7.rst
new file mode 100644
index 00000000000..1e9868073f7
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-05-28-22-49-59.bpo-33674.6LFFj7.rst
@@ -0,0 +1,4 @@
+Fix a race condition in SSLProtocol.connection_made() of asyncio.sslproto:
+start immediately the handshake instead of using call_soon(). Previously,
+data_received() could be called before the handshake started, causing the
+handshake to hang or fail.