We extend the revealed preference theory of consumer’s behavior originating in Samuelson’s Weak Axiom of Revealed Preference to simultaneously permit both non-singleton choice sets and random choice. We provide a consistency postulate for demand behavior when such behavior is represented in terms of a stochastic demand correspondence. When the consumer spends his or her entire wealth, our rationality postulate is equivalent to a condition we term “stochastic substitutability.” This equivalence generates as special cases in most of the basic results regarding consumers’ demand behavior in the existing revealed preference literature.