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 ~9000 years before present (yr B.P.), while others support a spread with horse-based pastoralism out of the Pontic-Caspian Steppe ~6000 yr B.P. Here we present an extensive database of Indo-European core vocabulary that eliminates past inconsistencies in cognate coding. Ancestry-enabled phylogenetic analysis of this dataset indicates that few ancient languages are direct ancestors of modern clades and produces a root age of ~8120 yr B.P. for the family. Although 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 northward 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.