Pyrenestes finches are unique among birds in showing a non-sex-determined polymorphism in bill size and are considered a textbook example of disruptive selection. Morphs breed randomly with respect to bill size, and differ in diet and feeding performance relative to seed hardness. Previous breeding experiments are consistent with the polymorphism being controlled by a single genetic factor. Here, we use genome-wide pooled sequencing to explore the underlying genetic basis of bill morphology and identify a single candidate region. Targeted resequencing reveals extensive linkage disequilibrium across a 300 Kb region containing the insulin-like growth factor 1 (IGF1) gene, with a single 5-million-year-old haplotype associating with phenotypic dominance of the large-billed morph. We find no genetic similarities controlling bill size in the well-studied Darwin's finches (Geospiza). Our results show how a single genetic factor may control bill size and provide a foundation for future studies to examine this phenomenon within and among avian species.