The occurrence of extrapair paternity (EPP) in socially monogamous species varies greatly among species and across latitudes. Recent work suggests that birds residing in less seasonal, tropical environments will have lower levels of EPP than seasonal tropical and temperate species. Less seasonal tropical birds are predicted to have the lowest rates of EPP because their presumed low breeding densities and low breeding synchrony may reduce the opportunities for extrapair mating, and their potentially higher adult survival and longer-term pair bonds may increase the costs of retaliation by males, resulting in reduced paternal care. Nevertheless, the limited number of studies in tropical regions impedes our understanding of whether EPP varies across environments and why. We report on rates of EPP and the potential underlying mechanisms for the observed rate in the Black-crowned Antshrike (Thamnophilus atrinucha, previously known as the Western Slaty Antshrike), a Neotropical and socially monogamous passerine residing in a relatively aseasonal environment. The birds had low rates of EPP, with 3% of offspring (3 of 89) in 4% of broods (2 of 50) being sired by extrapair males. Results are inconsistent with expectations that breeding density and variation in breeding synchrony influence EPP within the population, given the observed high density and high variation in breeding synchrony without simultaneous changes in EPP. The costs of retaliation by males, which provide extensive parental care, and the benefit of long-term pair bonds may lead to few females engaging in extrapair matings despite opportunities for doing so. Our results are consistent with predictions that aseasonal tropical species have lower EPP than seasonal tropical and temperate species.