We examine the role of stochastic feasibility in consumer choice using a random conditional choice set rule (RCCSR) and uniquely characterize the model from conditions on stochastic choice data. Feasibility is modeled to permit correlation in availability of alternatives. This provides a natural way to examine substitutability/complementarity. We show that an RCCSR generalizes the random consideration set rule of [Manzini and Mariotti, 2014]. We then relate this model to existing literature. In particular, an RCCSR is not a random utility model.