After a detailed look on the web, the only project I was able to find is Garbochess. It is BSD licensed, but it looks like it is not longer under development (latest commit was a year ago). I also was not able to find anything about the strength of the engine (ELO).
Major drawbacks JS has (in my opinion) are:
Well, technically, these are reasons why it would be hard to code a good chess engine - but who wants an engine with 1800 Elo? (Well, still enough for one or two standard deviations of players' practical purposes.)
And in the end: it's client side. If you need something client side, don't do it in a browser. If it can be done on the server, use it! E. g., using PHP, pipes and the UCI protocol, you'll get much further and you can let the server compute it for all clients (and I know it has been done before, but can't tell exactly where I've seen it).