Based on some reviews, I installed tChess Pro for US $7.99. I wasn't disappointed. While you can use the app to let two people play, I was more interested in playing against the computer. tChess Pro is a very strong opponent, but you can modify the levels that the game plays. It was the first time in a computer based chess game that I felt like I was playing a human, although at most levels except the lowest, I was getting clobbered.
The app allows you to set up games, add time controls, and there is an opening library mode that helps you understand the finer points of the game. You can take back moves, get a running analysis of your game, and get hints for the next move if you want them.
Other impressive features include the ability to email a game to someone, and you can choose from multiple board and chess piece designs. I especially liked the feature that allows you to use two fingers to rotate the board to any angle.
The game also contains built-in chess instructions; they are well written and a great place to start for beginners. It was the kind of thoughtful touch that makes the app rather special.
Some chess playing friends also praise Shredder Chess, which I haven't played but am going to look at soon. It has a similar feature set and is the same price. I have also enjoyed Deep Green for the iPhone, but it is not available in an iPad version yet.
One thing I didn't like is that the app icon displays semi-transparent chess pieces that aren't available as an option. I would have liked that set, and I think it was kind of misleading to showcase it in the icon. I wrote the program author, Tom Kerrigan, about that, and he told me that he tried to work out how to make such a set; the problem was that it would be so low contrast that it would basically be impossible to play on.
That may be true. It looks fine on the icon, and I'd like to see it added to the game. That's a small complaint for what really is an excellent chess opponent. The game is a universal binary, so it will also work fine on your iPhone or iPod touch.
There is another version of the app called tChess Lite. It is only US $0.99, and it is more for the casual enthusiast and doesn't play at the highest levels. If you are interested in chess and just getting started, it might be a good place to begin.
Here are a few screen captures: