Based primarily on the belief that Chromebook users would be better off sticking with Google's current CrOS kernel, I began testing 32-bit x86 Linux distros on my Acer C7. So far, the results of my experiments have been encouraging - not only does 32 bit Ubuntu 12.04.1 run without issues but it seems that most distros with Debian and/or Ubuntu lineage do as well. Results with other distros have been mixed. One key factor seems to be the use of initrd, which the CrOS kernel apparently does not support. Keep in mind that I'm only reporting that these distros install and boot using my method because I did not test them extensively.
x86 Distros on the C7
Here, I'll attempt to document my method so that others can benefit. IMHO, the distros I've highlighted represent the best match for the C7's hardware and resources.
In the meantime, I highly recommend checking out the Crouton script method developed by David Schneider. It essentially enables you to run Ubuntu as an application on CrOS. Credit for this find goes to Craig Errington.