Social monogamy has traditionally been suggested to be maintained because of weak sexual selection on male partner acquisition. However, the ubiquitous incidence of extra-pair paternity suggests that sexual selection can be strong in monogamous systems, although studies partitioning variance in male reproductive success have come to mixed conclusions. Here, we use detailed field data to examine variance in male reproductive success and its implications for the maintenance of sociality in a population of the socially monogamous lizard Egernia whitii. We show that both within-pair and, to a lesser extent, extra-pair partner acquisition contribute to the variance in male reproductive success, resulting in considerable opportunity for sexual selection. Despite this, levels of multiple mating are lower in Egernia compared to other reptiles, suggesting that male partner acquisition is constrained. We suggest that this constraint may be a result of strong territoriality combined with sexual conflict over multiple mating generated by costs of extra-pair paternity to females as a result of facultative male care. This has the potential to limit sexual selection by reducing variance in male reproductive success and therefore contribute to the maintenance of complex social organization.