LEKS, where males congregate to display and females attend only to mate, present one of the most remarkable outcomes of sexual selection1. It is a common but untested belief that females mate with the most vigorous males2. In leks of the black grouse Tetrao tetrix, males dominant in winter flocks were most successful in mating, as were males winning fights over female dummies placed at territory boundaries. Males tear feathers from each others' tail ornaments in combats, and attractive males always had undamaged tails. We report here that by choosing victorious males, females mate with males that are most likely to survive the following six months. There is a strong association between female preference and male viability which supports a basic assumption of the 'good gene' models (refs. 3-9) where choosy females benefit through better viability of their offspring. But females may also be choosing viable males for immediate benefits2,10, in particular if diseases can be transmitted during copulations.