Studying between-sex differences in body growth has strong implications for understanding life-history tactics of animals. We used age and carcass mass data from 2,312 female and 2,622 male alpine chamois (Rupicapra rupicapra) harvested in the French Alps to model the sex-specific body growth patterns of this species. Males were heavier (asymptotic body mass: 29.6 kg) than females (22.3 kg), with an adult sexual size dimorphism of 32.4%. Sexual size dimorphism originated from both differences in body growth after 1.5 years of age and differences in length of the growth period. Females reached asymptotic body mass almost 3 years earlier (3.5 years) than males (6.2 years). We also found that females 1st reproduced before achieving asymptotic growth, at 78% of their asymptotic body mass. Between-sex differences in growth patterns in this species are most likely due to stronger selection pressure for larger size in males than in females due to intrasexual competition.