D o electoral quotas for women alter women's chances of winning elections after they are withdrawn? I answer this question by examining an unusual natural experiment in India in which randomly chosen seats in local legislatures are set aside for women for one election at a time. Using data from Mumbai, I find that the probability of a woman winning office conditional on the constituency being reserved for women in the previous election is approximately five times the probability of a woman winning office if the constituency had not been reserved for women. I also explore tentative evidence on the mechanisms by which reservations affect women's ability to win elections. The data suggest that reservations work in part by introducing into politics women who are able to win elections after reservations are withdrawn and by allowing parties to learn that women can win elections.