This paper studies the effects of overconfidence in an investment-decision setting. A risk-averse agent privately observes information relevant to an investment decision, that he can report to a principal. In a standard common-priors setting, the optimal contract provides full insurance to the agent: the principal pays a fixed wage to the agent, asks him to reveal his information, and implements the efficient investment rule. When the agent overestimates the expected revenue of the project following investment, however, he is willing to wager on success against the (relatively pessimistic) principal, and hence bear some project risk in equilibrium. In addition, because what the principal considers to be the optimal investment rule is too conservative according to the agents beliefs and the agent holds some stake in the choice of investment rule, he will accept a lower fixed payment in exchange for a more liberal investment rule. This can be interpreted as giving more control to the agent. It is somewhat counterintuitive that the principal will surrender more control to an agent with whom she disagrees more sharply.