Hybridization allows adaptations to be shared among lineages and may trigger the evolution of new species1,2. However, convincing examples of homoploid hybrid speciation remain rare because it is challenging to demonstrate that hybridization was crucial in generating reproductive isolation3. Here we combine population genomic analysis with quantitative trait locus mapping of species-specific traits to examine a case of hybrid speciation in Heliconius butterflies. We show that Heliconius elevatus is a hybrid species that is sympatric with both parents and has persisted as an independently evolving lineage for at least 180,000 years. This is despite pervasive and ongoing gene flow with one parent, Heliconius pardalinus, which homogenizes 99% of their genomes. The remaining 1% introgressed from the other parent, Heliconius melpomene, and is scattered widely across the H. elevatus genome in islands of divergence from H. pardalinus. These islands contain multiple traits that are under disruptive selection, including colour pattern, wing shape, host plant preference, sex pheromones and mate choice. Collectively, these traits place H. elevatus on its own adaptive peak and permit coexistence with both parents. Our results show that speciation was driven by introgression of ecological traits, and that speciation with gene flow is possible with a multilocus genetic architecture.