Have you considered getting a playpen for him? I believe there is one for ferrets that comes with a bottom, which would make it possible to use a carpeted room if you are concerned about that (although chinchilla poop is relative dry and easy to clean up, and shouldn't damage carpet). You could also make your own playpen using large cardboard panels. You can order them from many shipping supply companies online, and you just tape the panels together. It's much cheaper than buying one, and they fold up easily for storage. You could use your bathroom, however you would have to make sure to thoroughly "chin-proof" the room (ie. covering the toilet, covering all wires, etc.). If he's able to get under the sink, it may not be the best place to play unless you can close it off some how.