We offer an explanation for the forward premium puzzle in foreign exchange markets based upon investor overconfidence. In the model, overconfident individuals overreact to their information about future inflation, which causes greater overshooting in the forward rate than in the spot rate. Thus, when agents observe a signal of higher future inflation, the consequent rise in the forward premium predicts a subsequent downward correction of the spot rate. The model can explain the magnitude of the forward premium bias and several other stylized facts related to the joint behavior of forward and spot exchange rates. Our approach is also consistent with the availability of profitable carry trade strategies.