ARM processors are common in recent ChromeOS devices.
Linux support for ARM Chromebooks is unfortunately rare. Difficulties include boot image incompatibilities with firmware bootloaders, Chromebook hardware support, and the fact that ARM is a second-class platform (at best) for most distros.
The distro with the most complete support for ARM Chromebooks is currently Arch Linux: http://archlinuxarm.org/.
Cadmium is an up and coming distro with support for several ARM Chromebooks not supported elsewhere: https://github.com/Maccraft123/Cadmium
Debian and Ubuntu also ship ARM packages, so it is within the realm of possibility (and a genuine goal) to add ARM support to GalliumOS. However, the project is not in progress at this time.
Another option for running Linux on an ARM ChromeOS device is Crouton.