This paper studies gender interactions within hierarchical organizations using a large data set on the duration of Italian municipal governments elected between 1993 and 2003. A municipal government can be viewed as a hierarchy, whose stability over time depends on the degree of cooperation between and within ranks. We find that in municipalities headed by female mayors, the probability of early termination of the legislature is higher. This result persists and becomes stronger when we control for municipality fixed effects as well as non-random sorting of women into municipalities using regression discontinuity in gender-mixed electoral races decided by a narrow margin. The likelihood that a female mayor survives until the end of her term is lowest when the council is entirely male, and in regions with less favorable attitudes towards working women. The evidence is suggestive that female mayors are less able at fostering cooperation among men, or alternatively, that men are more reluctant to be headed by women. Other interpretations receive less support in the data. Our results may provide an alternative explanation for the underrepresentation of women in leadership positions.