We consider the problem of interpolating missing observations in a time series modeled by a discrete‐time Markov chain. The general interpolation scheme involves a finite enumeration of all possible paths (i.e., admissible values for the missing data) and computation of the probability distribution of the paths. Procedures for the selection of a particular path are discussed in terms of a prespecified interpolation objective. In the special case of two‐state Markov chains, we investigate an efficient way of enumerating the paths based on the set of sufficient statistics. An example using daily rainfall occurrence series is presented.