Because many key career events, such as examinations and interviews, involve competition and stress, gender differences in response to these factors could help to explain the labor market gender gap. In a laboratory experiment, we manipulate psychosocial stress using the Trier Social Stress Test and confirm that this is effective by measuring salivary cortisol level and heart rate. Subjects perform in a real-effort task under both tournament and piece-rate incentives, and we elicit willingness to compete. We find that women under heightened stress perform worse than women in the control group when compensated with tournament incentives, whereas there is no treatment difference under piece-rate incentives. For men, stress does not affect output under competition or under piece rate. The gender gap in willingness to compete is not affected by stress, but stress decreases competitiveness overall, which is related to performance for women. Our results could explain gender differences in performance under competition, with implications for hiring practices and incentive structures in firms.