We present BRIEE, an algorithm for efficient reinforcement learning in Markov Decision Processes with block-structured dynamics (i.e., Block MDPs), where rich observations are generated from a set of unknown latent states. BRIEE interleaves latent states discovery, exploration, and exploitation together, and can provably learn a near-optimal policy with sample complexityscaling polynomially in the number of latent states, actions, and the time horizon, with no dependence on the size of the potentially infinite observation space.Empirically, we show that BRIEE is more sample efficient than the state-of-art Block MDP algorithm HOMER and other empirical RL baselines on challenging rich-observation combination lock problems which require deep exploration.