As if there isn't enough online chess around, here is another one for those who have a Facebook account. Simply called "Chess", it's actually an application that you can attach to your Facebook account. Play is turn-based so it's not like you'll have a gameboard similar to ICC or Playchess.
For the time being the app is beset with problems. Checkmates, for example, are recorded as just checks! I don't know if they've corrected that one. There are reports also of slow page loads. But the biggest problem is that you just can't seem to play. I've had this message since I added the app: "Chess is currently down to move server, will be up within the next few hours. Thank you!"