What say ye, Brits?

I'd say the Word Detective had it about right on the origin of "chum" as friend, Juan. It has a bit of a public school (private education, usually involving boarding) feel about it; quite a lot, actually. At the traditional boarding schools you would at some stage move up from a dormitory (dorm) to "chambers" - maybe at the really posh ones you'd never be in anything but chambers. But chambers would rarely be solo residences, you'd always share. And quite often you'd end up good friends with your chamber-mates; let's face it, they'd be as close to family as you'd get during school terms. Either you'd love them or hate them, I suspect.

Chamber-mate abbreviating to "chum" sounds vagely plausible to me, going via "chaymy" on to "chaym" then "ch'm".

Interesting that if you call someone a chum these days in England, more often than not you'd be expressing dislike and giving them a warning. "Now look here, chum".