This paper examines the problem of generating natural language descriptions of chess games. We introduce a new large-scale chess commentary dataset and propose methods to generate commentary for individual moves in a chess game. The introduced dataset consists of more than 298K chess move-commentary pairs across 11K chess games. We highlight how this task poses unique research challenges in natural language generation: the data contain a large variety of styles of commentary and frequently depend on pragmatic context. We benchmark various baselines and propose an end-to-end trainable neural model which takes into account multiple pragmatic aspects of the game state that may be commented upon to describe a given chess move. Through a human study on predictions for a subset of the data which deals with direct move descriptions, we observe that outputs from our models are rated similar to ground truth commentary texts in terms of correctness and fluency.