While sexual selection in mammals with female defense systems has historically received considerable attention, much less is known about the factors affecting reproductive success in mammalian species with scramble competition mating systems. Using mark-recapture techniques and DNA microsatellite loci to assign parentage, we examined the mating system and factors affecting the variation of the annual reproductive success in an introduced population of the Siberian chipmunk, Tamias sibiricus, a small, monomorphic, solitary squirrel. Our analyses showed that breeding females were spatially dispersed, setting the stage for a scramble competition mating system. Male reproductive success was positively associated with the size of the home range. The strength of sexual selection on this behavioral trait was very strong, equaling previous estimates for morphological traits in female defense mating systems. These findings suggest that a behavioral trait, space use, strongly influences the annual reproductive success in males, which is consistent with expectations in a scramble competition mating system. In both sexes, reproductive success was influenced by habitat, with twice as many juveniles produced in semiopen than in closed habitat, possibly due to differences in food availability between the two habitats.