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In this paper, a novel method for estimating the parameters of multiple chirp signals in additive Gaussian white noise is proposed. The method combines a global optimization theorem with a new Markov chain Monte Carlo algorithm, called the simulated annealing one-variable-at-a-time random walk Metropolis-Hastings algorithm. It is a computationally modest implementation of maximum likelihood estimation and has no error propagation effect. Simulation results show that the proposed method can give good estimates for the unknown parameters, even when the parameters of the individual chirp signals are closely spaced and the Cramer-Rao lower bound can be attained even at low signal-to-noise ratio.