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In this paper, we consider the general multiple-target tracking problem in which an unknown number of targets appears and disappears at random times and the goal is to find the tracks of targets from noisy observations. We propose an efficient real-time algorithm that solves the data association problem and is capable of initiating and terminating a varying number of tracks. We take the data-oriented, combinatorial optimization approach to the data association problem but avoid the enumeration of tracks by applying a sampling method called Markov chain Monte Carlo (MCMC). The MCMC data association algorithm can be viewed as a "deferred logic" method since its decision about forming a track is based on both current and past observations. At the same time, it can be viewed as an approximation to the optimal Bayesian filter. The algorithm shows remarkable performance compared to the greedy algorithm and the multiple hypothesis tracker (MHT) under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates.