pip crashes at startup importing from OpenSSL

For python-openssl Version: 0.15.1-2build1 on Ubuntu 16.04

'pip' (and other commands) importing from OpenSSL crash with the following traceback

$ pip
Traceback (most recent call last):
  File "/usr/bin/pip", line 9, in <module>
    from pip import main
  File "/usr/lib/python2.7/dist-packages/pip/__init__.py", line 13, in <module>
    from pip.exceptions import InstallationError, CommandError, PipError
  File "/usr/lib/python2.7/dist-packages/pip/exceptions.py", line 6, in <module>
    from pip._vendor.six import iteritems
  File "/usr/lib/python2.7/dist-packages/pip/_vendor/__init__.py", line 64, in <module>
    vendored("cachecontrol")
  File "/usr/lib/python2.7/dist-packages/pip/_vendor/__init__.py", line 36, in vendored
    __import__(modulename, globals(), locals(), level=0)
  File "/usr/share/python-wheels/CacheControl-0.11.5-py2.py3-none-any.whl/cachecontrol/__init__.py", line 9, in <module>
  File "/usr/share/python-wheels/CacheControl-0.11.5-py2.py3-none-any.whl/cachecontrol/wrapper.py", line 1, in <module>
  File "/usr/share/python-wheels/CacheControl-0.11.5-py2.py3-none-any.whl/cachecontrol/adapter.py", line 3, in <module>
  File "/usr/share/python-wheels/requests-2.9.1-py2.py3-none-any.whl/requests/__init__.py", line 53, in <module>
  File "/usr/share/python-wheels/urllib3-1.13.1-py2.py3-none-any.whl/urllib3/contrib/pyopenssl.py", line 54, in <module>
  File "/usr/lib/python2.7/dist-packages/OpenSSL/__init__.py", line 8, in <module>
    from OpenSSL import rand, crypto, SSL
  File "/usr/lib/python2.7/dist-packages/OpenSSL/SSL.py", line 118, in <module>
    SSL_ST_INIT = _lib.SSL_ST_INIT
AttributeError: 'module' object has no attribute 'SSL_ST_INIT'

By googling the last line, it seems many people are experiencing this problem (an example https://stackoverflow.com/questions/43267157/python-attributeerror-module-object-has-no-attribute-ssl-st-init).