This paper addresses the problem of maximum likelihood sequence estimation (MLSE) based on a hidden reciprocal chain (HRC) as the underlying target model. HRCs are non-causal, discrete-time finite-state stochastic processes which can be regarded as the one-dimensional version of a Markov random field, although they are not in general Markov processes. This paper describes a procedure for evaluating the MLSE for a HRC and compares the resultant estimator with its Markov Model equivalent: the Viterbi algorithm. In addition, the performance of the newly proposed reciprocal MLSE is compared to a HRC-based optimal smoother.