Stockfish should run just fine on a Chromebook. It's also the strongest chess engine in the world presently. You just need a compatible chess program to run it on.
Chess engine for Chromebook

Chromebook was designed for browsing, hence the name CHROMEbook. Google Chrome is a browser.
Indeed. It was hard enough figuring out how to open a PGN file!

Why would anyone want a Chromebook?
It's ideal for someone like my father who only uses a laptop for checking his emails and playing solitare. Something like a thinkpad (what I have) would be a waste of money for him because of his very limited computer skills.

Why would anyone want a Chromebook?
Cheap and it does everything I want it to, except for this, apparently :)
The Best analysis engine for Chrome OS (chomrebooks, chromeboxes..) is lichess. It is online-based, and provide a decent analysises for your games. I think it uses bits of the strongest engines out there so as to provide something decent for all players.
Just copy/past your PGN file here and enjoy:
Chromebook was designed for browsing, hence the name CHROMEbook. Google Chrome is a browser.
True, but chromebooks can in fact do more than just web browsing. But a lot of people doesn't know it. You have a file manager, a native video player that can play various types of files locally on the computer and a bunch of preloaded apps. But yeah, Google rely on the web as THE platform and hence doesn't need a full-fledged OS running legacy softares. But isn't live/online chess mostly web-based anyway? With a membership on chess.com you get pretty much all the tools that are needed to become a decent chess player. What's missing are the most powerful engines bundled as web apps but until then, lichess isn't bad by any mean..

Just for people who hate on the chromebook/ for people like me who have older cpu's
they can be useful despite the obvious limitations. Compared 2 nice labtops are they cheap, i only paid 150 dollars for mine (on sale) and i can use youtube @ twitch/ running whenever i want/ both are sites which will slow down my computer, they work well for just web browsing. Also (stockfish) for Lichess is a great resource, u can change the settings to show 4 lines of infinite analysis/ u might have to write down your own notes and lines on a separate folder though
later dudes
goommba88

chroombooks suck i try to do anything on them and they fail
*Chromebooks, I* It sounds like you have a skill issue on knowing your chromebook, check the manual, just read it, AND KNOW IT.

I know very little about how my Chromebook works, much less which chess engine it would run best or where to find one. Who's the smart guy with the answers?