Speckle noise reduction is a prerequisite task in images captured by ultrasonography systems due to their inherent noisy nature. In this work, we propose a new despeckling method in the contourlet domain using the Cauchy prior. The multiplicative speckle noise is first transferred to an additive one using a logarithmic transform. The logarithmically-transformed contourlet coefficients of the image and noise are assumed to be the Cauchy and Maxwell distributions, respectively. In order to estimate the noise-free contourlet coefficients, an efficient closed-form Bayesian maximum a posteriori estimator is developed. Simulations are carried out to evaluate the performance of the proposed despeckling method by using the synthetically-speckled and real ultrasound images. It is shown that the proposed method outperforms several existing techniques in terms of the signal-to-noise ratio and is able to preserve the diagnostically signific ant details of the ultrasound images.