Okay, I found lichess.org . Sounds promising:

Free, open source
Accounts are optional
you can make groups (we could have an ot.com group)
looks nice, clean, and minimalist, the way I like it
their computer engine named Stockfish mated me in less than 20 seconds, here's my game

[Event "Casual game"]
[Site "http://lichess.org/6a57cox3"]
[Date "2013.12.11"]
[White "Anonymous"]
[Black "AI-level-1"]
[Result "0-1"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "26"]
[Variant "Standard"]

1. c4 Na6 2. Nc3 Nf6 3. h4 d5 4. Rh3 e5 5. Rf3 e4 6. Rf5 Bxf5 7. Nxe4 Nxe4 8. b3 Bb4 9. Nf3 dxc4 10. Ng5 cxb3 11. Ne6 Bxe6 12. Qxb3 Bxd2+ 13. Bxd2 Qxd2# 0-1