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.