The consequences of the Neolithic transition in Europe--one of the most important cultural changes in human prehistory--is a subject of great interest. However, its effect on prehistoric and modern-day people in Iberia, the westernmost frontier of the European continent, remains unresolved. We present, to our knowledge, the first genome-wide sequence data from eight human remains, dated to between 5,500 and 3,500 years before present, excavated in the El Portalón cave at Sierra de Atapuerca, Spain. We show that these individuals emerged from the same ancestral gene pool as early farmers in other parts of Europe, suggesting that migration was the dominant mode of transferring farming practices throughout western Eurasia. In contrast to central and northern early European farmers, the Chalcolithic El Portalón individuals additionally mixed with local southwestern hunter-gatherers. The proportion of hunter-gatherer-related admixture into early farmers also increased over the course of two millennia. The Chalcolithic El Portalón individuals showed greatest genetic affinity to modern-day Basques, who have long been considered linguistic and genetic isolates linked to the Mesolithic whereas all other European early farmers show greater genetic similarity to modern-day Sardinians. These genetic links suggest that Basques and their language may be linked with the spread of agriculture during the Neolithic. Furthermore, all modern-day Iberian groups except the Basques display distinct admixture with Caucasus/Central Asian and North African groups, possibly related to historical migration events. The El Portalón genomes uncover important pieces of the demographic history of Iberia and Europe and reveal how prehistoric groups relate to modern-day people.