Berkson errors are commonplace in empirical microeconomics. In consumer demand this form of measurement error occurs when the price an individual pays is measured by the (weighted) average price paid by individuals in a group (e.g., a county), rather than the true transaction price. We show the importance of Berkson errors for demand estimation with nonseparable unobserved heterogeneity. We develop a consistent estimator using external information on the true price distribution. Examining gasoline demand in the U.S., we document substantial within-market price variability. Accounting for Berkson errors is quantitatively important. Imposing the Slutsky shape constraint reduces sensitivity to Berkson errors.