The females of many Old World primate species produce prominent and conspicuous swellings of the perineal skin around the time of ovulation. These sexual swellings have been proposed to increase competition among males for females(1) or to increase the likelihood of a female getting fertilized, by signalling either a female's general reproductive status(1-5), or the timing of her ovulation(6). Here we show that sexual swellings in wild baboons reliably advertise a female's reproductive value over her lifetime, in accordance with a theoretical model of honest signalling(7). Females with larger swellings attained sexual maturity earlier, produced both more offspring and more surviving offspring per year than females with smaller swellings, and had a higher overall proportion of their offspring survive. Male baboons use the size of the sexual swelling to determine their mating effort, fighting more aggressively to consort females with larger swellings, and spending more time grooming these females. Our results document an unusual case of a sexually selected ornament in females, and show how males, by mating selectively on the basis of the size of the sexual swelling, increase their probability of mating with females more likely to produce surviving offspring.