The origin of contemporary Europeans remains contentious. We obtained a genome sequence from Kostenki 14 in European Russia dating from 38,700 to 36,200 years ago, one of the oldest fossils of anatomically modern humans from Europe. We find that Kostenki 14 shares a close ancestry with the 24,000-year-old Mal'ta boy from central Siberia, European Mesolithic hunter-gatherers, some contemporary western Siberians, and many Europeans, but not eastern Asians. Additionally, the Kostenki 14 genome shows evidence of shared ancestry with a population basal to all Eurasians that also relates to later European Neolithic farmers. We find that Kostenki 14 contains more Neandertal DNA that is contained in longer tracts than present Europeans. Our findings reveal the timing of divergence of western Eurasians and East Asians to be more than 36,200 years ago and that European genomic structure today dates back to the Upper Paleolithic and derives from a metapopulation that at times stretched from Europe to central Asia.