ChessSensei

Free two player chess game.

The game is released under GPLv3. Full source available at https://github.com/neural99/chesssensei

Missing features:

+ NO AI

+ NO NETWORK MULTIPLAY

On the other hand:

+ No ads

+ No special permissions

+ Full enforcing of standard chess rules

App icon is licenced under the GPL and was downloaded from: https://www.iconfinder.com/icons/7159/board_game_chess_icon

Chess piece icons are from Wikipedia, licensed under the GPL.