Mate choice based on sexual ornaments can impose strong selection, which raises the question of how genetic variation in ornaments is maintained. One mechanism that has been proposed is genic capture. If ornament expression is influenced by general condition and condition is under polygenic control, selection will be inefficient in removing genetic variation. Here we analyze whether the genetic architecture of beak color in a population of zebra finches supports this hypothesis. Zebra finch beak color is commonly assumed to be under strong selection by mate choice, although some of the evidence is ambiguous. We show that beak redness has a heritability of 34% in our population and that it is strongly genetically correlated between the sexes, suggesting that it is largely controlled by the same genes in males and females. We mapped variation in beak redness based on 1404 single-nucleotide polymorphism (SNP) markers genotyped in a large pedigree. We find evidence for linkage on four chromosomes (Tgu1, Tgu5, Tgu13, Tgu21), which together explain a large part of the additive genetic variance. Our finding of genomic regions with major additive effects is not consistent with directional selection and genic capture, but rather suggests a role of antagonistic pleiotropy in maintaining genetic variation.