Hybrid zones provide one of the more prickly challenges to the cherished biological species concept, which is based on reproductive isolation between species, because some hybrid zones occur in areas where recognised species come together and mate to produce viable progeny. By contrast, hybrid zones have repeatedly provided outstanding material for the study of evolution: they allow us to study ecological and genomic differences between recently diverged taxa; and they bring into sharp focus the interplay between migration, selection, recombination and drift. A new theoretical analysis now demonstrates that hybrid-zone dynamics provide a counterintuitive explanation for how a new chromosomal sex-determination system can evolve and spread across the landscape, displacing the ancestral system, even though it would be eliminated by natural selection in a single isolated population. This work thus provides a provocative resolution to a conundrum that has puzzled cytogeneticists and evolutionary biologists for years.