Reinforcement learning (RL) provides a framework for learning goal-directed policies given user-specified rewards. However, since designing rewards often requires substantial engineering effort, we are interested in the problem of learning without rewards, where agents must discover useful behaviors in the absence of task-specific incentives. Intrinsic motivation is a family of unsupervised RL techniques which develop general objectives for an RL agent to optimize that lead to better exploration or the discovery of skills. In this paper, we propose a new unsupervised RL technique based on an adversarial game which pits two policies against each other to compete over the amount of surprise an RL agent experiences. The policies each take turns controlling the agent. The Explore policy maximizes entropy, putting the agent into surprising or unfamiliar situations. Then, the Control policy takes over and seeks to recover from those situations by minimizing entropy. The game harnesses the power of multi-agent competition to drive the agent to seek out increasingly surprising parts of the environment while learning to gain mastery over them. We show empirically that our method leads to the emergence of complex skills by exhibiting clear phase transitions. Furthermore, we show both theoretically---via a latent state space coverage argument---and empirically that our method has the potential to be applied to the exploration of stochastic, partially-observed environments. We show that Adversarial Surprise learns more complex behaviors, and explores more effectively than competitive baselines, outperforming intrinsic motivation methods based on active inference, novelty-seeking (Random Network Distillation (RND)), and multi-agent unsupervised RL (Asymmetric Self-Play (ASP)) in MiniGrid, Atari and VizDoom environments.