We exploit a natural experiment based on the Italian promotion system for associate and full professor positions to investigate gender differences in the willingness to enter competition. Using data on about 42,000 professors and controlling for productivity and a number of individual and field characteristics, we find that females have a lower probability of applying for competition of about 4 percentage points. The determinants of this gap seem to be gender differences in risk-aversion and self-confidence and women's fear of discrimination: the lower tendency to enter competition is especially relevant for women in the lower tail of the distribution of scientific productivity and in fields in which productivity is not easily measurable; furthermore, women are less likely to apply for promotion in fields in which promotions of females in the past were rare.