Heterogeneity in choice models is typically assumed to have a normal distribution in both Bayesian and classical setups. In this paper, we propose a semiparametric Bayesian framework for the analysis of random coefficients discrete choice models that can be applied to both individual as well as aggregate data. Heterogeneity is modeled using a Dirichlet process prior which varies with consumers characteristics through covariates. We develop a Markov chain Monte Carlo algorithm for fitting such model, and illustrate the methodology using two different datasets: a household level panel dataset of peanut butter purchases, and supermarket chain level data for 31 ready-to-eat breakfast cereals brands.