We consider the problem of online planning in a Markov decision process with discounted rewards for any given initial state. We consider the PAC sample com-plexity problem of computing, with probability 1−δ, an -optimal action using the smallest possible number of calls to the generative model (which provides reward and next-state samples). We design an algorithm, called StOP (for Stochastic-Optimistic Planning), based on the "optimism in the face of uncertainty" princi-ple. StOP can be used in the general setting, requires only a generative model, and enjoys a complexity bound that only depends on the local structure of the MDP.