We propose a model of individual choice behavior that makes joint predictions about the probability distribution of choices and decision times. In our model the agent receives noisy signals about the utility of the alternatives and optimally chooses when to stop learning and make a decision. We show that it is optimal to stop whenever the signal crosses a barrier that is decreasing in time; this is in contrast to the drift-diffusion models (DDM) used in cognitive sciences, which have constant barriers. We show that our model implies a different relationship between the distributions of choices and decision times: the agent decides faster conditional on choosing the ex post optimal item and makes slower decisions conditional on choosing a suboptimal item (the DDM equates those decision times); also, his choices are faster conditional on the two items having an ex post small utility difference (the DDM overpredicts those decision times). (With Drew Fudenberg and Philipp Strack.)