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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 and evolutionary loss 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 quantitative trait locus (QTL) that explains ~5% of the overall variation in the trait. Using a series of approaches, we narrow this large QTL interval to several likely candidate genes, including genes involved in fin regeneration and growth. Furthermore, we find evidence of selection on ancestry at one of these candidates in four natural hybrid populations, consistent with selection against the sword in these populations.