Seems I have the same problem, just posted a topic about it (didn't see this one): http://www.chess.com/forum/view/help-support/22-crashes-on-ios-313 . Hope some staffmember can respond.
Updated app doesn't load on iPad
I have the same problem with the Chess.com app on my iPod Touch (1st gen 16gb, iOS v3.1.3). I try to launch it and it crashes and closes back up. I thought it might have been in some weird state, so I deleted the app. Turned off the iPod, turned it back on (full power cycle) and then went to the app store and downloaded it again. Same issue - crashes before I can do anything -- quite quickly, in fact.
Anybody have trouble loading updated app on iPad?