There are two native chess apps now. Caissa mentioned above and one called simply Chess.
Caissa looks just a tad prettier, little more detail on the pieces etc. But Chess plays better in my opinion, mostly because in Chess you tap a piece once to select it (as the one you want to move) and tap again on the target location you want to move to, and it works well. Whereas Caissa uses a sort of hold and drag action to move a piece, and it's erratic - sometimes snaps back and seems to refuse your desired move (even when it's a legal move) and also sometimes snaps a piece to a landing square you didn't want.
To see the chess app you may need to add the Robota Softwarehouse source - which is worthwhile anyway, as they also produce several other very good apps ....