Flightlessness in birds is the product of changes in suites of characters-including increased body size and reduced anterior limbs-that have evolved repeatedly and independently under similar ecological conditions (generally insularity). It remains unknown whether this phenotypic convergence extends to the genomic level, partially because many losses of flight occurred long ago (such as in penguins or ratites), thus complicating the study of the genetic pathways to flightlessness. Here, we use genome sequencing to study the evolution of flightlessness in a group of ducks that are current and dynamic exemplars of this major functional transition. These recently diverged Tachyeres steamer ducks differ in their ability to fly: one species is predominantly flighted and three are mainly flightless. Through a genome-wide association analysis, we identify two narrow candidate genomic regions implicated in the morphological changes that led to flightlessness, and reconstruct the number of times flightlessness has evolved in Tachyeres. The strongest association is with DYRK1A, a gene that when knocked out in mice leads to alterations in growth and bone morphogenesis. These findings, together with phylogenetic and demographic analyses, imply that the genomic changes leading to flightlessness in Tachyeres may have evolved once, and that this trait remains functionally polymorphic in two species. © 2019 The Author(s). Evolution © 2019 The Society for the Study of Evolution.