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Existing hidden Markov models focus on mean regression for the longitudinal response. However, the tails of the response distribution are as important as the center in many substantive studies. We propose a quantile hidden Markov model to provide a systematic method to examine the entire conditional distribution of the response given the hidden state and potential covariates. Instead of considering homogeneous hidden Markov models, which assume that the probabilities of between-state transitions are independent of subject- and time-specific characteristics, we allow the transition probabilities to depend on exogenous covariates, thereby yielding nonhomogeneous Markov chains and making the proposed model more flexible than its homogeneous counterpart. We develop a Bayesian approach coupled with efficient Markov chain Monte Carlo methods for statistical inference. Simulations are conducted to assess the empirical performance of the proposed method. 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