This paper uses Bayesian estimation techniques to uncover the central bank preferences of the big five Latin American inflation targeting countries: Brazil, Chile, Colombia, Mexico, and Peru. The target weights of each central bank's loss function are estimated using a medium-scale small open economy New Keynesian model with incomplete international asset markets and imperfect exchange-rate pass-through. Our results suggest that all central banks in the region place a high priority on stabilizing inflation and interest rate smoothing. While stabilizing the real exchange rate is a concern for all countries except Brazil, only Mexico is found to assign considerable weight to reducing real exchange rate fluctuations. Overall, Brazil, Colombia, and Peru show evidence of implementing a strict inflation targeting policy, whereas Chile and Mexico follow a more flexible policy by placing a sizeable weight to output gap stabilization. Finally, the posterior distributions for the central bank preference parameters are found to be strikingly different under complete asset markets. This highlights the sensitivity of Bayesian estimation, particularly when uncovering central bank preferences, to alternative international asset market structures.