Although some lineages of animals and plants have made impressive adaptive radiations when provided with ecological opportunity, the propensities to radiate vary profoundly among lineages for unknown reasons. In Africa's Lake Victoria region, one cichlid lineage radiated in every lake, with the largest radiation taking place in a lake less than 16,000 years old. We show that all of its ecological guilds evolved in situ. Cycles of lineage fusion through admixture and lineage fission through speciation characterize the history of the radiation. It was jump-started when several swamp-dwelling refugial populations, each of which were of older hybrid descent, met in the newly forming lake, where they fused into a single population, resuspending old admixture variation. Each population contributed a different set of ancient alleles from which a new adaptive radiation assembled in record time, involving additional fusion-fission cycles. We argue that repeated fusion-fission cycles in the history of a lineage make adaptive radiation fast and predictable.