Dating the onset of deep-water flow between the Arctic and North Atlantic oceans is critical for modelling climate change in the Northern Hemisphere and for explaining changes in global ocean circulation throughout the Cenozoic era (from about 65 million years ago to the present). In the early Cenozoic era, exchange between these two ocean basins was inhibited by the Greenland-Scotland ridge, but a gateway through the Faeroe-Shetland basin has been hypothesized. Previous estimates of the date marking the onset of deep-water circulation through this basin-on the basis of circumstantial evidence from neighbouring basins-have been contradictory, ranging from about 35 to 15 million years ago. Here we describe the newly discovered Southeast Faeroes drift, which extends for 120 km parallel to the basin axis. The onset of deposition in this drift has been dated to the early Oligocene epoch ( approximately 35 million years ago) from a petroleum exploration borehole. We show that the drift was deposited under a southerly flow regime, and conclude that the initiation of deep-water circulation from the Norwegian Sea into the North Atlantic Ocean took place much earlier than is currently assumed in most numerical models of ancient ocean circulation.