Competition involves two main dimensions, a rivalry for resources and the ranking of relative performance. If socially recognized, the latter yields a ranking in terms of social status. The rivalry for resources resulting from competitive incentives has been found to negatively affect women's performance relative to that of men. However, little is known about gender differences in the performance consequences of social-status ranking. In our experiments we introduce a novel design that allows us to isolate the effects of status ranking from those caused by a rivalry for resources. Subjects do a time-limited task where they need to search for numbers and add them up. Performance is straightforwardly measured by the number of correct summations. When there is no status ranking we find no gender differences in the number of attempted summations or in performance. By contrast, when there is status ranking men significantly increase the number of attempted summations as well as the number of correct summations. Remarkably, when women are subjected to status ranking, they significantly decrease the number of attempted summations. The net result is striking. With status ranking men attempt more summations and correctly solve many more than women. These differences are markedly large and statistically highly significant. Our results suggest that increased participation in competitive environments could harm women's labor market success along a hidden channel.