I downloaded the source tar file for Python 3.5.1 and compiled.  Upon running make test, it fails at

test_networked_good_cert (test_httplib.HTTPSTest) ... ERROR

Abbreviated Traceback looks like:

======================================================================
ERROR: test_networked_good_cert (test_httplib.HTTPSTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/tmp/bennet/Python-3.5.1/Lib/test/test_httplib.py", line 1325, in test_networked_good_cert
    h.request('GET', '/')
. . . .
  File "/tmp/local/python-3.5.1/lib/python3.5/ssl.py", line 628, in do_handshake
    self._sslobj.do_handshake()
ssl.SSLError: [SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:645)

I have replicated this on CentOS 7, RHEL 6.5, and Ubuntu 16.04 Xenial with GCC versions 4.8.5, 4.8.5, and 5.3.1, respectively.

There was a previous bug reported about expired certificates that was closed.  It appears that it's using CERT_localhost, defined at the top to be keycert.pem, and that appears to be valid:

[bennet@flux-build-centos7-dev test]$ openssl x509 -in keycert.pem -text
Certificate:
    Data:
        Version: 3 (0x2)
        Serial Number: 15548457918976213582 (0xd7c7381919afc24e)
. . . .
        Validity
            Not Before: Oct  8 23:01:56 2010 GMT
            Not After : Oct  5 23:01:56 2020 GMT

I can replicate the test outside of make with the attached script.

I tried to be complete reporting and searching for this first; I apologize if I missed an obvious solution.