We present an algorithm, HOMER, for exploration and reinforcement learning in rich observation environments that are summarizable by an unknown latent state space. The algorithm interleaves representation learning to identify a new notion of kinematic state abstraction with strategic exploration to reach new states using the learned abstraction. The algorithm provably explores the environment with sample complexity scaling polynomially in the number of latent states and the time horizon, and, crucially, with no dependence on the size of the observation space, which could be infinitely large. This exploration guarantee further enables sample-efficient global policy optimization for any reward function. On the computational side, we show that the algorithm can be implemented efficiently whenever certain supervised learning problems are tractable. Empirically, we evaluate HOMER on a challenging exploration problem, where we show that the algorithm is more sample efficient than standard reinforcement learning baselines.