This paper considers the role of gender in generating inequality of opportunity. Using data on long-run income for Swedish men and women, we explore to what extent income inequality is due to circumstances beyond individuals' control, such as gender and parental income, rather than to differences in individuals' choices. The key idea is that a society has achieved equality of opportunity if there is no income inequality that is due to circumstances. Analyzing men and women separately, we find that circumstances account for up to 31% of income inequality among men and up to 25% among women. We conclude that there is greater equality of opportunity among women than among men. When we analyze men and women together, treating gender as a circumstance, at most 38% of income inequality can be attributed to circumstances. Gender accounts for up to 13% of income inequality, making gender the single most important circumstance in accounting for inequality in long-run income in Sweden.