Contingency (or 'luck') in early life plays an important role in shaping individuals' development. When individuals live within larger societies, social experiences may cause the importance of early contingencies to be magnified or dampened. Here we test the hypothesis that competition magnifies the importance of early contingency in a sex-specific manner by comparing the developmental trajectories of genetically identical, free-living mice who either experienced high levels of territorial competition (males) or did not (females). We show that male territoriality results in a competitive feedback loop that magnifies the importance of early contingency and pushes individuals onto divergent, self-reinforcing life trajectories, while the same process appears absent in females. Our results indicate that the strength of sexual selection may be self-limiting, as within-sex competition increases the importance of early life contingency, thereby reducing the ability of selection to lead to evolution. They also demonstrate the potential for contingency to lead to dramatic differences in life outcomes, even in the absence of any underlying differences in ability ('merit').