Despite being the fundamental primitive of the study of decision-making in economics, choice correspondences are not observable: even for a single menu of options, we observe at most one choice of an individual at a given point in time, as opposed to the set of all choices she deems most desirable in that menu. However, it may be possible to observe a person choose from a feasible menu at various times, repeatedly. We propose a method of inferring the choice correspondence of an individual from this sort of choice data. First, we derive our method axiomatically, assuming an ideal dataset. Next, we develop statistical techniques to implement this method for real-world situations where the sample at hand is often fairly small. As an application, we use the data of two famed choice experiments from the literature to infer the choice correspondences of the participating subjects.