The transition from the Middle to the Upper Palaeolithic, approximately 40,000-35,000 radiocarbon years ago, marks a turning point in the history of human evolution in Europe. Many changes in the archaeological and fossil record at this time have been associated with the appearance of anatomically modern humans. Before this transition, the Neanderthals roamed the continent, but their remains have not been found in the northernmost part of Eurasia. It is generally believed that this vast region was not colonized by humans until the final stage of the last Ice Age some 13,000-14,000 years ago. Here we report the discovery of traces of human occupation nearly 40,000 years old at Mamontovaya Kurya, a Palaeolithic site situated in the European part of the Russian Arctic. At this site we have uncovered stone artefacts, animal bones and a mammoth tusk with human-made marks from strata covered by thick Quaternary deposits. This is the oldest documented evidence for human presence at this high latitude; it implies that either the Neanderthals expanded much further north than previously thought or that modern humans were present in the Arctic only a few thousand years after their first appearance in Europe.