We study a multi-task principal-agent problem in which tasks can be in direct conflict with each other. In theory, it is difficult to induce a single agent to exert efforts in two conflicting tasks, because effort in one task decreases the success probability of the other task. We have conducted an experiment in which we find strong support for the relevance of this incentive problem. In the presence of conflict, subjects choose two efforts significantly less often when both tasks are assigned to a single agent than when there are two agents each in charge of one task.