The short answer is "sorry, it won't work." BUT that is oversimplified. CHIRP is written in Python and is supported on three OSs: Linux, Windows, and MacOS. Not on chromebook. You have three options: 1) Learn how to run Python on Chromebook natively, 2) Learn how to run Linux on Chromebook, or 3) use a really inexpensive (less than $40) Linux computer in addition to your Chromebook. Of the three the last one by far easiest unless your skill level is a lot higher that it appears from your question, but I may be miss-judging. So:
a) Purchase a Raspberry PI (or other fine little Linux computer).
b) Purchase or re-purpose a microSD card of at leas 4GB.
c) get on the web and learn.
The other two approaches involve placing your Chromebook in developer mode and doing a fair amount of learning and magic, For Linux the magic is called "Crouton". That's the "Linux capability" you mentioned. If you follow the Crouton instructions, you will get to a Linux command line prompt. From there, you can follow the CHIRP generic Linux instructions to download and run CHIRP. If you to your Linux prompt and can then get no further, please comeback here for help.