We consider a Markov decision process with deterministic state transition dynamics, adversarially generated rewards that change arbitrarily from round to round, and a bandit feedback model in which the decision maker only observes the rewards it receives. In this setting, we present a novel and efficient online decision making algorithm named MarcoPolo. Under mild assumptions on the structure of the transition dynamics, we prove that MarcoPolo enjoys a regret of O(T 3/4√ log T) against the best deterministic policy in hindsight. Specifically, our analysis does not rely on the stringent unichain assumption, which dominates much of the previous work on this topic.