The origins of the Indo-European language family are hotly disputed. Bayesian phylogenetic analyses of core vocabulary have produced conflicting results, with some supporting a farming expansion out of Anatolia c. 9000 BP, while others support a spread with horse-based pastoralism out of the Pontic-Caspian Steppe c. 6000 BP. Here we present an extensive new database of Indo-European core vocabulary that eliminates past inconsistencies in cognate coding. Ancestry-enabled phylogenetic analysis of our new dataset indicates that few ancient languages are direct ancestors of modern clades, and produces a root age for the family of c. 8120 BP. While this date is not consistent with the Steppe hypothesis, it does not rule out an initial homeland south of the Caucasus, with a subsequent branch northwards onto the Steppe and then across Europe. We reconcile this “hybrid hypothesis” with recently published ancient DNA evidence from the Steppe and the northern Fertile Crescent.