We study the impact of board gender quotas on the labor market for corporate directors. We find that the annual rate of turnover of female directors falls by about a third following the introduction of a quota in France in 2011. This decline in turnover is more pronounced for new appointments induced by the quota, and for appointments made by firms that regularly hire directors who are members of the French business elite. By contrast, the quota has no effect on male director turnover. The evidence suggests that, by changing the director search technology used by firms, the French quota has improved the stability of director-firm matches.