The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm in applied microeconomics. However, as is well known, it is not possible to infer the structure of preferences in the absence of assumptions on the structure of noise. We show that the difficulty can be overcome if data sets are enlarged to include response times. A simple condition on response time distributions (a weaker version of first-order stochastic dominance) ensures that choices reveal preferences without assumptions on the structure of utility noise. Standard random utility models from economics and standard drift-diffusion models from psychology generate data sets fulfilling this condition. Sharper results are obtained if the analysis is restricted to specific classes of noise. Under symmetric noise, response times allow to uncover preferences for choice pairs outside the data set, and if noise is Fechnerian, precise choice probabilities can be forecast out-of-sample. We apply our tools to an experimental data set, illustrating that the application is simple and generates a remarkable prediction accuracy.