I wrote an (still incomplete) chess app a while ago. Might be the perfect opponent for you... 
Ok, the app was crapp, but it was quite well structured, so we could port it on various platform, like Swing, J2ME and even the Palm pilot.
I wasn't wanting to play against a machine, but what I would be interested in is a well-designed system that allows players across the internet to play each other. By well-designed, I mean it needs to be polished and look good, as well as having useful features such as a last-move history, a (minimally) animated opponent move indicator (to catch your attention if you happen to glance away), and other bits and pieces. Ok, the app was crapp, but it was quite well structured, so we could port it on various platform, like Swing, J2ME and even the Palm pilot.
lichess.org is open source and completely viable for use in a bitcoin competition. I was using it for the core of a site I was developing, BitChess.com a while back but ended up hitting the inevitable wall of "it's impossible to make a chess site where people can't cheat".
Who will win??