diff --git a/CHANGES/3355.bugfix b/CHANGES/3355.bugfix
new file mode 100644
index 00000000000..fd002cb00df
--- /dev/null
+++ b/CHANGES/3355.bugfix
@@ -0,0 +1 @@
+Fixed a transport is :data:`None` error -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/connector.py b/aiohttp/connector.py
index bf40689d81b..2499a2dabe9 100644
--- a/aiohttp/connector.py
+++ b/aiohttp/connector.py
@@ -1121,6 +1121,9 @@ async def _start_tls_connection(
                 f"[{type_err!s}]"
             ) from type_err
         else:
+            if tls_transport is None:
+                msg = "Failed to start TLS (possibly caused by closing transport)"
+                raise client_error(req.connection_key, OSError(msg))
             tls_proto.connection_made(
                 tls_transport
             )  # Kick the state machine of the new TLS protocol