diff --git a/quiche/quic/masque/masque_server_backend.cc b/quiche/quic/masque/masque_server_backend.cc
index 8e74e16..b42a055 100644
--- a/quiche/quic/masque/masque_server_backend.cc
+++ b/quiche/quic/masque/masque_server_backend.cc
@@ -88,6 +88,19 @@
       request_headers, request_body, request_handler);
 }
 
+void MasqueServerBackend::HandleConnectHeaders(
+    const spdy::Http2HeaderBlock& request_headers,
+    RequestHandler* request_handler) {
+  if (MaybeHandleMasqueRequest(request_headers, request_handler)) {
+    // Request was handled as a MASQUE request.
+    return;
+  }
+  QUIC_DLOG(INFO) << "Fetching non-MASQUE CONNECT response for "
+                  << request_headers.DebugString();
+  QuicMemoryCacheBackend::HandleConnectHeaders(request_headers,
+                                               request_handler);
+}
+
 void MasqueServerBackend::CloseBackendResponseStream(
     QuicSimpleServerBackend::RequestHandler* request_handler) {
   QUIC_DLOG(INFO) << "Closing response stream";
diff --git a/quiche/quic/masque/masque_server_backend.h b/quiche/quic/masque/masque_server_backend.h
index 8f35c3b..a862097 100644
--- a/quiche/quic/masque/masque_server_backend.h
+++ b/quiche/quic/masque/masque_server_backend.h
@@ -39,6 +39,8 @@
       const spdy::Http2HeaderBlock& request_headers,
       const std::string& request_body,
       QuicSimpleServerBackend::RequestHandler* request_handler) override;
+  void HandleConnectHeaders(const spdy::Http2HeaderBlock& request_headers,
+                            RequestHandler* request_handler) override;
 
   void CloseBackendResponseStream(
       QuicSimpleServerBackend::RequestHandler* request_handler) override;