  We study a two-player, zero-sum, stochastic game with incomplete information
on one side in which the players are allowed to play more and more frequently.
The informed player observes the realization of a Markov chain on which the
payoffs depend, while the non-informed player only observes his opponent's
actions. We show the existence of a limit value as the time span between two
consecutive stages vanishes; this value is characterized through an auxiliary
optimization problem and as the solution of an Hamilton-Jacobi equation.
