I think you'd find yourself pretty limited. There doesn't seem to be a lot of chess software out there for Chromebooks so you'd be stuck with strictly web based stuff. Keep us posted. I'd love to be proved wrong as I really like the looks of some of them.
Playing chess on a chromebook/chromebox

Love my Toshiba chromebook but it's not a chess machine...you're limited to just web stuff. Which is not bad - I mean, here we are talking chess on the web. You can certainly do some chess-related work because there are lots of web-based tools but it'd all be web-based.
Keep in mind the processor in most of them is designed for supporting web browsing, not doing computations.
Hi,
I would like to get some perspectives by people who play chess on these computers, does it work well?
I intend to buy the Asus chromebox, it's inexpensive and the hardware is quite decent so that's interesting.
See: http://www.amazon.com/Asus-CHROMEBOX-M004U-ASUS-Desktop/dp/B00IT1WJZQ/ref=sr_1_sc_1?ie=UTF8&qid=1430096698&sr=8-1-spell&keywords=asus+hcromebox
Would you buy a Chrome OS machine for playing chess?