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 what a person chooses 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 is often small. A special case of this methodology allows for the estimation of individual preferences from repeated pairwise choice data. To demonstrate the applicability of the method, we use it on the data of a famous experiment (Tversky, 1969) on transitivity of preferences. We find that the conclusions this data leed to are more nuanced than the original ones.