Let X = {X n } n∈IN be a hidden process and Y = {Y n } n∈IN be an observed process. We assume that (X,Y) is a (pairwise) Markov Chain (PMC). PMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient parameter estimation and Bayesian restoration algorithms. In this paper we propose a fast (i.e., O(N)) algorithm for computing the entropy of {X n } N n=0 given an observation sequence {y n } N n=0 .