Understanding why some evolutionary lineages generate exceptionally high species diversity is an important goal in evolutionary biology. Haplochromine cichlid fishes of Africa's Lake Victoria region encompass >700 diverse species that all evolved in the last 150,000 years. How this `Lake Victoria Region Superflock' could evolve on such rapid timescales is an enduring question. Here, we demonstrate that hybridization between two divergent lineages facilitated this process by providing genetic variation that subsequently became recombined and sorted into many new species. Notably, the hybridization event generated exceptional allelic variation at an opsin gene known to be involved in adaptation and speciation. More generally, differentiation between new species is accentuated around variants that were fixed differences between the parental lineages, and that now appear in many new combinations in the radiation species. We conclude that hybridization between divergent lineages, when coincident with ecological opportunity, may facilitate rapid and extensive adaptive radiation.