Several countries have recently introduced gender quotas in hiring and promotion committees at universities. This paper studies whether these policies increase the presence of women in top academic positions. The identification strategy exploits the random assignment mechanism in place between 2002 and 2006 in all academic disciplines in Spain to select the members of promotion committees. We find that a larger proportion of female evaluators increases the chances of success of female applicants to full professor positions.The magnitude of the effect is large: each additional woman on a committee composed of seven members increases the number of women promoted to full professor by 14%. Conversely, when committee members decide on promotions to associate professor positions, we do not observe any significant interaction between the gender of evaluators and the gender of candidates. If anything, in this case a larger share of female evaluators is associated with fewer successful female applicants. The evidence is consistent with the existence of ambivalent sexism.