We study maximum entropy correlated equilibria (Maxent CE) in multi-player games. After motivating and deriving some interesting important properties of Maxent CE, we provide two gradient-based algorithms that are guaranteed to converge to it. The proposed algorithms have strong connections to algorithms for statistical estimation (e.g., iterative scaling), and permit a distributed learning-dynamics interpretation. We also briefly discuss possible connections of this work, and more generally of the Maximum Entropy Principle in statistics, to the work on learning in games and the problem of equilibrium selection.