We study the identification and estimation of Gorman-Lancaster style hedonic models of demand for differentiated products for the case when one product characteristic is not observed. Our identification and estimation strategy is a two-step approach in the spirit of Rosen (1974). Relative to Rosens approach, we generalize the first stage estimation to allow for a single dimensional unobserved product characteristic, and also allow the hedonic pricing function to have a general, non-additive structure. In the second stage, if the product space is continuous and the functional form of utility is known then there exists an inversion between the consumers choices and her preference parameters. This inversion can be used to recover the distribution of random coefficients nonparametrically. For the more common case when the set of products is finite, we use the revealed preference conditions from the hedonic model to develop a Gibbs sampling estimator for the distribution of random coefficients. We apply our methods to estimating personal computer demand.