Title: Learning Chess Blindfolded. Abstract: Transformer language models have made tremendous strides in natural language understanding. However, the complexity of natural language makes it challenging to ascertain how accurately these models are tracking the world state underlying the text. Motivated by this issue, we consider the task of language modeling for the game of chess.  Unlike natural language, chess notations describe a simple, constrained, and deterministic domain. Moreover, we observe that chess notation itself allows for directly probing the world state, without requiring any additional probing-related machinery.  Additionally, we have access to a vast number of chess games coupled with the exact state at every move, allowing us to measure the impact of various ways of including grounding during language model training. Overall, we find that with enough training data, transformer language models can learn to track pieces and predict legal moves when trained solely from move sequences. However, in adverse circumstances (small training sets or prediction following long move histories), providing access to board state information during training can yield consistent improvements.