Crouton on USB 3.0 Drive?

I got a chromebook and I want to do some programming on it, and because there is no C IDE out there where I can compile I am a bit stuck.
Is it possible to run it like Crouton that is native to your system with the xiwi setup?
So basically I want Crouton on a USB drive that is permanent storage and can be run via Xiwi.

Many Thanks!