DISCLAIMER: This could all quite plausibly brick your Chromebook, and I take no responsibility for any damage you might inflict on it or yourself. Follow along at your own risk.
Most Chromebooks can run some flavour of GNU/Linux using the Chrubuntu method, running off the kernel that comes with ChromeOS. I found, however, that the ChromeOS kernel didn’t play well with recent X.org versions, and would refuse to recover from suspend, and not deal very well at all with having an external screen attached to it.
I also wanted to replace ChromeOS entirely with Arch on my Chromebook, because only 16 gigabytes of eMMC isn’t very convenient for dual booting. To accomplish this, I needed an external installation medium.
First of all, you’ll need to get your Chromebook into developer mode if you haven’t already. This is model specific, although for most recent models holding the Escape and Reload keys while booting should do the trick. If not, ask Google.