That's the NEXT thing that's happening! :)
New iPad app

Just played my first Live games on the iPad, it's magnificent!
The board maximizes the real estate on the iPad with a very clean look and very rapid piece response. (Go to Settings to disable the 'Submit' button, I did.)
During the first game I was disconnected and the app quit, but I reopened the app and my game was still in progress. Nice, and crucial for mobile games which can temporarily lose signal.
Also, I found it necessary to first delete the previous Chess.com app from both my computer and iPad before being able to successfully download the new app.
Live Chess on the iPad! Boom goes the dynamite!

I note that the badge on the icon does not work on my iPad1.
It does on my iPhone.
Is it a known iPad problem ?

Stéphane, I've got the opposite problem. For me it works well on my iPad (3, and 1 before it), but not well on my iPhone (3GS). All have been running the latest iOS 5.1.
I wonder if many others are having this problem - perhaps there is some kind of technical or program issue with pushing the notifications to multiple devices tied to the same chess.com account?

Historically, yes, we've seen issues with trying to get notifications working faithfully on two different devices for the same account. And it's not just our app, either. Generally, I enable Notifications on my phone, but not on the 'pad.
Related: the next update will support Notification Center & feature a non-annoying custom alert sound. :)
Feedback: I absolutely love it! However, I'd love to be able to chat via live chat on the iPad. Can that happen?