When choice is stochastic, revealed preference analysis often relies on random utility models. However, it is impossible to infer preferences without assumptions on the distribution of utility noise. We show that this difficulty can be overcome by using response time data. A simple condition on response time distributions ensures that choices reveal preferences without distributional assumptions. Standard models from economics and psychology generate data fulfilling this condition. Sharper results are obtained under symmetric or Fechnerian noise, where response times allow uncovering preferences or predicting choice probabilities out of sample. Application of our tools is simple and generates remarkable prediction accuracy.