Python 3 is now standard for ARCH Linux.
That has nothing to do with it. If you can't also install a python 2 runtime, then you need to get a different distro. Python 3 is part of the standard install of Ubuntu too, but they also include a Python 2 runtime because so many things still require it (anything that uses pygtk, for starters).
Is there a beta version of CHIR that works under python 3?
No. Python 3 is not compatible with Python 2, and PyGTK will never be ported to Python 3. Making CHIRP support Python 3 will require a substantial rewrite of its entire UI to use the new bindings. It will happen someday, but not any time soon.
Google for "python 3 pygtk" and you'll see a lot of similar confusion.
Looks like all you have to do is install the python2 package in Arch:
https://wiki.archlinux.org/index.php/python
...and as I said, arrange for chirp to be run by /usr/bin/python2 instead of /usr/bin/python.
--Dan