Stockfish Chess for iOS is a free app based on the comprehensive open-source Stockfish chess engine.
The app claims to be much stronger than most commercial chess programs, but you're able to adjust this and choose between several styles of play-- anything from "Passive" to "Suicidal".
There are several playing modes. You can play against the computer; play both sides yourself; set up particular board positions, and optionally display book moves and engine analysis, including search depth, evaluations and main lines.
Stockfish Chess has several piece sets and colour schemes to choose from, too, although they all look quite plain. The app is more about playing power than carefully rendered 3D pawns.
It's not been updated for a while, but then neither has chess, and overall Stockfish Chess is still a good choice for anyone looking for a challenging game.