The way I solved this is by running
$ python -m ensurepip
Which produced a stacktrace ending with this line:
FileNotFoundError: [Errno 2] No such file or directory: '/usr/lib64/python3.4/ensurepip/_bundled/setuptools-20.10.1-py2.py3-none-any.whl'
So I went to https://pypi.python.org/pypi/setuptools/20.10.1 and grabbed the wheel and put it in my directory (which I had to create with
mkdir -p /usr/lib64/python3.4/ensurepip/_bundled/)
python -m ensurepip again I was confronted with
No such file or directory: '/usr/lib64/python3.4/ensurepip/_bundled/pip-8.1.1-py2.py3-none-any.whl
So I went to https://pypi.python.org/pypi/pip/8.1.1, grabbed that wheel and stuck it in the directory.
Now I can create virtualenvs with
python -m venv .venv. Success!