We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLMs), a new method of nonparametric regression that accommodates continuous and categorical inputs, models a response variable locally by a generalized linear model. We give conditions for the existence and asymptotic unbiasedness of the DP-GLM regression mean function estimate; we then give a practical example for when those conditions hold. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression including regression trees and Gaussian processes.