Supergenes are tight clusters of loci that facilitate the co-segregation of adaptive variation, providing integrated control of complex adaptive phenotypes(1). Polymorphic supergenes, in which specific combinations of traits are maintained within a single population, were first described for 'pin' and 'thrum' floral types in Primula(1) and Fagopyrum(2), but classic examples are also found in insect mimicry(3-5) and snail morphology(6). Understanding the evolutionary mechanisms that generate these co-adapted gene sets, as well as the mode of limiting the production of unfit recombinant forms, remains a substantial challenge(7-10). Here we show that individual wing-pattern morphs in the polymorphic mimetic butterfly Heliconius numata are associated with different genomic rearrangements at the supergene locus P. These rearrangements tighten the genetic linkage between at least two colour-pattern loci that are known to recombine in closely related species(9-11), with complete suppression of recombination being observed in experimental crosses across a 400-kilobase interval containing at least 18 genes. In natural populations, notable patterns of linkage disequilibrium (LD) are observed across the entire P region. The resulting divergent haplotype clades and inversion breakpoints are found in complete association with wing-pattern morphs. Our results indicate that allelic combinations at known wing-patterning loci have become locked together in a polymorphic rearrangement at the P locus, forming a supergene that acts as a simple switch between complex adaptive phenotypes found in sympatry. These findings highlight how genomic rearrangements can have a central role in the coexistence of adaptive phenotypes involving several genes acting in concert, by locally limiting recombination and gene flow.