This paper sets up a rational inattention model for the choice of departure time for a traveler facing random travel time. In this model, the traveler chooses in advance an information strategy for the travel time outcome, and then chooses departure time each day given the information received that day. The model describes how cheaper information allows the traveler to expand his/her consideration set and adapt more flexibly to changing conditions. This increases the traveler's payoff. The marginal cost of travel time variability is always positive. The ability to choose the information strategy reduces the cost of travel time variability compared to neoclassical travelers whose information is exogenously given.