This paper describes a method for estimating random coefficient discrete choice models that is both flexible and simple to compute. We demonstrate that, with a finite number of types,
choice probabilities are a linear function of the model parameters. Because of this linearity,
our model can be estimated using linear regression subject to inequality constraints. We can approximate an arbitrary distribution of random coefficients by allowing the number of types to be sufficiently large. Therefore, we say our estimator is nonparametric for the distribution of heterogeneity.