In this paper, we propose and test a stochastic model of consumer choice that incorporates attribute-based variety seeking. Our stochastic variety-seeking model (SVS) has nested within it a fixed variety-seeking model, a zero-order model of choice, and a first-order (''pure variety'') model. We compare the SVS model to alternative models. Under stochastic variety seeking, we examine the nature of the variety sought and provide a test of the ''station'' hypothesis. Unlike fixed variety-seeking models, our model allows variety seeking to vary in intensity and consistency over individuals as well as over purchase occasions. We show that the model is equivalent to a random utility model with the features that the attributes of brands relative to those of the brand previously bought influence choice, and the extent of variety seeking is random over choice occasions for a given individual. The model permits a closed-form solution to the conditional switching probabilities parameterized by variety-seeking parameters, and dependent on brand attributes. We apply our model to individual choice data obtained from a field study specifically designed for the purpose at hand.