It might be useful to expose SSL_get_verify_result, https://wiki.openssl.org/index.php/Manual:SSL_get_verify_result(3) . The function returns the last verification error of 0 for no error. Application could still verify the chain with verify_mode = CERT_NONE.

>>> import socket, ssl
>>> ctx = ssl.SSLContext()
>>> s = ctx.wrap_socket(socket.socket())
>>> s.connect(('www.python.org', 443))
>>> s._sslobj._sslobj.get_verify_result()
(20, 'unable to get local issuer certificate')