Hidden Markov models using Gaussian mixture models as their hidden state distributions have been successfully applied in text-dependent speaker identification applications. Nevertheless, it is well-known that Gaussian mixture models are very vulnerable to the presence of outliers in the fitting set used for their estimation. Student's-t mixture models have been proposed recently as a heavy-tailed, tolerant to outliers alternative to Gaussian mixture models. In this paper we exploit the robustness of student's-t mixture models in the context of hidden Markov models by introducing a new hidden Markov chain model where the hidden state distributions are student's-t mixture models. We experimentally show that our model outperforms competing text-dependent speaker identification techniques.