Right now your choices for Chromebooks that support Linux are pretty limited. The Google Pixelbook and the Samsung Chrome Plus have been the first devices to support it. Today however, the team over at XDA has discovered that the new HP Chromebook X2 is now supported.
Linux support on the X2 is limited to the Chrome OS Canary Channel. For those that aren’t familiar with Chrome OS’ channels, the Canary Channel is pre-alpha essentially with a lot of experimentation (and thus crashes) going on. It is not for the faint of heart and indeed you have to bypass a lot of the platforms security mechanisms to get to it. But if you really want to go there, you can and can try out Linux on the X2.