We propose InfoChess, a symmetric adversarial game that elevates competitive information acquisition to the primary objective. There is no piece capture, removing material incentives that would otherwise confound the role of information. Instead, pieces are used to alter visibility. Players are scored on their probabilistic inference of the opponent's king location over the duration of the game. To explore the space of strategies for playing InfoChess, we introduce a hierarchy of heuristic agents defined by increasing levels of opponent modeling, and train a reinforcement learning agent that outperforms these baselines. Leveraging the discrete structure of the game, we analyze gameplay through natural information-theoretic characterizations that include belief entropy, oracle cross entropy, and predictive log score under the action-induced observation channel. These measures disentangle epistemic uncertainty, calibration mismatch, and uncertainty induced by adversarial movement. The design of InfoChess renders it a testbed for studying multi-agent inference under partial observability. We release code for the environment and agents, and a public interface to encourage further study.