Most previous analytical works on the performance of space-time block coded systems are based on perfect channel estimation at the receiver, which is impossible in practice. In this paper, we present a maximum-likelihood (ML) receiver jointly with channel estimation for a space-time orthogonal block coded system. Based on this receiver structure, we derive exact, closed-form expressions as well as light upper bounds for the bit error rate (BER) with MPSK modulation over the slow, nonselective, Rayleigh fading channel. Our BER expressions show directly the dependence of the BER on the mean square error of the channel estimator. Simulation results using a Wiener filter as the channel estimator for Jakes' Rayleigh fading model are obtained to demonstrate the accuracy of the analysis.