The genetic changes responsible for evolutionary transitions from generalist to specialist phenotypes are poorly understood. Here we examine the genetic basis of craniofacial traits enabling novel trophic specialization in a sympatric radiation of Cyprinodon pupfishes endemic to San Salvador Island, Bahamas. This recent radiation consists of a generalist species and two novel specialists: a small-jawed "snail-eater" and a large-jawed "scale-eater." We genotyped 12 million single nucleotide polymorphisms (SNPs) by whole-genome resequencing of 37 individuals of all three species from nine populations and integrated genome-wide divergence scans with association mapping to identify divergent regions containing putatively causal SNPs affecting jaw size-the most rapidly diversifying trait in this radiation. A mere 22 fixed variants accompanied extreme ecological divergence between generalist and scale-eater species. We identified 31 regions (20 kb) containing variants fixed between specialists that were significantly associated with variation in jaw size which contained 11 genes annotated for skeletal system effects and 18 novel candidate genes never previously associated with craniofacial phenotypes. Six of these 31 regions showed robust signs of hard selective sweeps after accounting for demographic history. Our data are consistent with predictions based on quantitative genetic models of adaptation, suggesting that the effect sizes of regions influencing jaw phenotypes are positively correlated with distance between fitness peaks on a complex adaptive landscape.