Worm-like snakes (scolecophidians) are small, burrowing species with reduced vision. Although largely neglected in vertebrate research, knowledge of their biogeographical history is crucial for evaluating hypotheses of snake origins. We constructed a molecular dataset for scolecophidians with detailed sampling within the largest family, Typhlopidae (blindsnakes). Our results demonstrate that scolecophidians have had a long Gondwanan history, and that their initial diversification followed a vicariant event: the separation of East and West Gondwana approximately 150 Ma. We find that the earliest blindsnake lineages, representing two new families described here, were distributed on the palaeolandmass of India+Madagascar named here as Indigascar. Their later evolution out of Indigascar involved vicariance and several oceanic dispersal events, including a westward transatlantic one, unexpected for burrowing animals. The exceptional diversification of scolecophidians in the Cenozoic was probably linked to a parallel radiation of prey (ants and termites) as well as increased isolation of populations facilitated by their fossorial habits.