We generalize the stochastic revealed preference methodology of McFadden and Richter (1990) for finite choice sets to settings with limited consideration. Our approach is nonparametric and requires partial choice set variation. We impose a monotonicity condition on attention first proposed by Cattaneo et al. (2020) and a stability condition on the marginal distribution of preferences. Our framework is amenable to statistical testing. These new restrictions extend widely known parametric models of consideration with heterogeneous preferences.