Consider the Hidden Markov model where the realization of a single Markov chain is observed by a number of noisy sensors. The sensor scheduling problem for the resulting hidden Markov model is as follows: design an optimal algorithm for selecting at each time instant, one of the many sensors to provide the next measurement. Each measurement has an associated measurement cost. The problem is to select an optimal measurement scheduling policy, so as to minimize a cost function of estimation errors and measurement costs. The problem of determining the optimal measurement policy is solved via stochastic dynamic programming. Numerical results are presented.