In many animal societies where hierarchies govern access to reproduction, the social rank of individuals is related to their age and weight and slow-growing animals may lose their place in breeding queues to younger 'challengers' that grow faster. The threat of being displaced might be expected to favour the evolution of competitive growth strategies, where individuals increase their own rate of growth in response to increases in the growth of potential rivals. Although growth rates have been shown to vary in relation to changes in the social environment in several vertebrates including fish and mammals, it is not yet known whether individuals increase their growth rates in response to increases in the growth of particular reproductive rivals. Here we show that, in wild Kalahari meerkats (Suricata suricatta), subordinates of both sexes respond to experimentally induced increases in the growth of same-sex rivals by raising their own growth rate and food intake. In addition, when individuals acquire dominant status, they show a secondary period of accelerated growth whose magnitude increases if the difference between their own weight and that of the heaviest subordinate of the same sex in their group is small. Our results show that individuals adjust their growth to the size of their closest competitor and raise the possibility that similar plastic responses to the risk of competition may occur in other social mammals, including domestic animals and primates.