Biologists since Darwin have been fascinated by the evolution of sexually selected ornaments, particularly those that reduce viability. Uncovering the genetic architecture of these traits is key to understanding how they evolve and are maintained. Here, we investigate the genetic architecture of a sexually selected ornament, the “sword” fin extension that characterizes many species of swordtail fish (Xiphophorus). Using sworded and swordless sister species of Xiphophorus, we generated a mapping population and show that the sword ornament is polygenic – with ancestry across the genome explaining substantial variation in the trait. After accounting for the impacts of genome-wide ancestry, we identify one major effect QTL that explains ∼5% of the overall variation in the trait. Using a series of approaches, we narrow this large QTL interval to a handful of likely candidate genes, including the gene sp8. Notably, sp8 plays a regulatory role in fin regeneration and harbors several derived substitutions that are predicted to impact protein function in the species that has lost the sword ornament. Furthermore, we find evidence of selection on ancestry at sp8 in four natural hybrid populations, consistent with selection against the sword in these populations.