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It has been shown that electropherograms of DNA sequences can be modeled with hidden Markov models. Basecalling, the procedure that determines the sequence of bases from the given electropherogram can then be performed using the Viterbi algorithm. A training step is required prior to basecalling in order to estimate the HMM parameters. In this paper, we propose a Bayesian approach which employs the Markov chain Monte Carlo (MCMC) method to perform basecalling. Such an approach not only allows one to naturally encode the prior biological knowledge into the basecalling algorithm, it also exploits both the training data and the basecalling data in estimating the HMM parameters, leading to more accurate estimates. Using the recently sequenced genome of the organism Legionella pneumophila, we show that the MCMC basecaller outperforms the state-of-the-art basecalling algorithm in terms of total errors while requiring much less training than other proposed statistical basecallers.