The shift from hunter-gathering to food production, the so-called Neolithic Revolution, profoundly changed human societies. Whilst much is known about the mode of spread of people and domesticates into Europe during the Neolithic period, the origin of this cultural package in the Ancient Near East and Anatolia is poorly understood. By sequencing the whole genome (1.39x) of an early Neolithic woman from Ganj Dareh, in the Zagros Mountains of Iran, we show that the eastern part of the Ancient Near East was inhabited by a population genetically most similar to hunter-gatherers from the Caucasus but distinct from the Neolithic Anatolian people who later brought food production into Europe. Despite their key role in developing the Neolithic package, the inhabitants of Ganj Dareh made little direct genetic contribution to modern European populations, suggesting they were somewhat isolated from other populations in this region. Their high frequency of short runs of homozygosity, comparable to other early Neolithic farmers, suggests that they overwintered the Last Glacial Maximum in a climatically favourable area, where they may have received a genetic contribution from a population basal to modern Eurasians. Thus, the Neolithic package was developed by at least two genetically-distinct groups which coexisted next to each other, implying a degree of cultural yet little genetic exchange among them.