Women's underrepresentation in leadership positions has been well documented, but the reasons behind it are not well understood. We carry out a field experiment to test a prominent theory about the source of the gender gap in leadership ambition: women's higher aversion to competitive environments. Using politics as a context for our study, we employ two distinct subject pools - highly politically active individuals and workers from an online labor market. We find that priming individuals to consider the competitive nature of politics has a strong negative effect on women's interest in political office, but not on men's interest, hence significantly increasing the gender gap in leadership ambition.