The Eocene and Oligocene epochs (~55 to 23 million years ago) comprise a critical phase in Earth history. An array of geological records supported by climate modelling indicates a profound shift in global climate during this interval, from a state that was largely free of polar ice caps to one in which ice sheets on Antarctica approached their modern size. However, the early glaciation history of the Northern Hemisphere is a subject of controversy. Here we report stratigraphically extensive ice-rafted debris, including macroscopic dropstones, in late Eocene to early Oligocene sediments from the Norwegian-Greenland Sea that were deposited between about 38 and 30million years ago. Our data indicate sediment rafting by glacial ice, rather than sea ice, and point to East Greenland as the likely source. Records of this type from one site alone cannot be used to determine the extent of ice involved. However, our data suggest the existence of (at least) isolated glaciers on Greenland about 20million years earlier than previously documented, at a time when temperatures and atmospheric carbon dioxide concentrations were substantially higher.