Addressing female underrepresentation in leadership positions has become a key policy objective. However, little is known about the extent to which leadership appeals differently to women. Collecting new data from a large firm, I document that women are substantially less likely to apply for early-career promotions. Realized application patterns and large-scale surveys reveal the role of an understudied feature of promotions -- having to assume responsibility over a team -- which is less appealing to women. This gender difference is not accounted for by standard explanations, such as success likelihood or confidence, but is rather a product of common design features of leadership positions.