diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index ade7ef5..bed0d41 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -4764,6 +4764,28 @@ def msg_cb(conn, direction, version, content_type, msg_type, data):
             msg
         )
 
+    def test_msg_callback_deadlock_bpo43577(self):
+        client_context, server_context, hostname = testing_context()
+        server_context2 = testing_context()[1]
+
+        def msg_cb(conn, direction, version, content_type, msg_type, data):
+            pass
+
+        def sni_cb(sock, servername, ctx):
+            sock.context = server_context2
+
+        server_context._msg_callback = msg_cb
+        server_context.sni_callback = sni_cb
+
+        server = ThreadedEchoServer(context=server_context, chatty=False)
+        with server:
+            with client_context.wrap_socket(socket.socket(),
+                                            server_hostname=hostname) as s:
+                s.connect((HOST, server.port))
+            with client_context.wrap_socket(socket.socket(),
+                                            server_hostname=hostname) as s:
+                s.connect((HOST, server.port))
+
 
 def test_main(verbose=False):
     if support.verbose:
diff --git a/Misc/NEWS.d/next/Library/2021-03-21-10-13-17.bpo-43577.m7JnAV.rst b/Misc/NEWS.d/next/Library/2021-03-21-10-13-17.bpo-43577.m7JnAV.rst
new file mode 100644
index 0000000..a7db48b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-03-21-10-13-17.bpo-43577.m7JnAV.rst
@@ -0,0 +1 @@
+Fix deadlock when using :class:`ssl.SSLContext` debug callback with :meth:`ssl.SSLContext.sni_callback`.
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index bea144c..f3c3b20 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -2202,6 +2202,11 @@ static int PySSL_set_context(PySSLSocket *self, PyObject *value,
         Py_INCREF(value);
         Py_SETREF(self->ctx, (PySSLContext *)value);
         SSL_set_SSL_CTX(self->ssl, self->ctx->ctx);
+        /* Set SSL* internal msg_callback to state of new context's state */
+        SSL_set_msg_callback(
+            self->ssl,
+            self->ctx->msg_cb ? _PySSL_msg_callback : NULL
+        );
 #endif
     } else {
         PyErr_SetString(PyExc_TypeError, "The value must be a SSLContext");
diff --git a/Modules/_ssl/debughelpers.c b/Modules/_ssl/debughelpers.c
index b840da2..af56f9d 100644
--- a/Modules/_ssl/debughelpers.c
+++ b/Modules/_ssl/debughelpers.c
@@ -23,6 +23,7 @@ _PySSL_msg_callback(int write_p, int version, int content_type,
     ssl_obj = (PySSLSocket *)SSL_get_app_data(ssl);
     assert(PySSLSocket_Check(ssl_obj));
     if (ssl_obj->ctx->msg_cb == NULL) {
+        PyGILState_Release(threadstate);
         return;
     }