The late survival of archaic hominin populations and their long contemporaneity with modern humans is now clear for southeast Asia. In Europe the extinction of the Neanderthals, firmly associated with Mousterian technology, has received much attention, and evidence of their survival after 35kyrBP has recently been put in doubt. Here we present data, based on a high-resolution record of human occupation from Gorham's Cave, Gibraltar, that establish the survival of a population of Neanderthals to 28kyrBP. These Neanderthals survived in the southernmost point of Europe, within a particular physiographic context, and are the last currently recorded anywhere. Our results show that the Neanderthals survived in isolated refuges well after the arrival of modern humans in Europe.