We study the steady state of an overlapping generations economy where singles search for spouses. In our model economy men and women live for many years and they differ in their fecundity, in their earnings, and in their survival probabilities. These three features are age-dependent and deterministic. Singles meet at random. They propose when the expected value of their current match exceeds that of remaining single. If both partners propose, the meeting ends up in a marriage. Marriages last until death does them apart, widows and widowers never remarry, and people make no other economic decisions whatsoever. In our model economy people marry because they value companionship, bearing children, and sharing their income with their spouses. The matching function depends on the single sex-ratios which are endogenous. Our model economy has only two free parameters: the search friction and the utility share of bearing children. We choose their values to match the median ages of first-time brides and grooms. We show that modeling the marriage decision in this simple way is sufficient to account for the age distributions of ever and never married men and women, for the probabilities of marrying a younger bride and a younger groom, and for the age distributions of first births observed in the United States in the year 2000. The previous literature on this topic claims that marriage is a waiting game in which women are choosier than men, and old and rich pretenders outbid the young and poor ones in their competition for fecund women. In this article we tell a different story. We show that their shorter biological clocks make women uniformly less choosy than men of the same age. This turns marriage into a rushing game in which women are willing to marry older men because delaying marriage is too costly for women. Our theory predicts that most of the gender age difference at first marriage will persist even if the gender wage-gap disappears. It also predicts that the advances in the reproductive technologies will play a large role in reducing the age difference at first marriage.