A generalized theory of revealed preference is formulated for choice situations where the consequences of choices from given menus are uncertain. In a nonprobabilistic framework, rational choice behavior can be defined by requiring the existence of a preference relation on the set of possible consequences and an extension rule for this relation to the power set of the set of consequences such that the chosen sets of possible outcomes are the best elements in the feasible set according to this extension rule. Rational choice is characterized under various assumptions on these relations.