We study cheating as a collective-risk social dilemma in a group setting in which individuals are asked to report their actual outcomes. Misreporting their outcomes increases the individual's earnings but when the sum of claims in the group reaches a certain threshold, a risk of collective sanction affects all the group members, regardless of their individual behavior. Because of the pursuit of selfish interest and a lack of coordination with other group members, the vast majority of individuals eventually earn less than the reservation payoff from honest reporting in the group. Over time, most groups are trapped in a "Tragedy of Dishonesty", despite the presence of moral costs of lying. The risk of collective sanction is triggered less frequently in small groups than in large ones, while priming a collectivist mindset has little effect on lying.