The Hymenoptera have arrhenotokous haplodiploidy in which males normally develop from unfertilized eggs and are haploid, while females develop from fertilized eggs and are diploid. Multiple sex determination systems are known to underlie haplodiploidy, and the best understood is single-locus complementary sex determination (sl-CSD) in which sex is determined at a single polymorphic locus. Individuals heterozygous at the sex locus develop as females; individuals that are hemizygous (haploid) or homozygous (diploid) at the sex locus develop as males. sl-CSD can be detected with inbreeding experiments that produce diploid males in predictable proportions as well as sex ratio shifts due to diploid male production. This sex determination system is considered incompatible with inbreeding because the ensuing increase in homozygosity increases the production of diploid males that are inviable or infertile, imposing a high cost on matings between close relatives. However, in the solitary hunting wasp Euodynerus foraminatus, a species suspected of having sl-CSD, inbreeding may be common due to a high incidence of sibling matings at natal nests. In laboratory crosses with E. foraminatus, we find that sex ratios and diploid male production (detected as microsatellite heterozygosity) are consistent with sl-CSD, but not with other sex determination systems. This is the first documented example of sl-CSD in a hymenopteran with an apparent natural history of inbreeding, and thus presents a paradox for our understanding of hymenopteran genetics.