North Atlantic climate is very sensitive to overturning in the Greenland-Iceland-Norwegian (GIN) Seas, overflow of deep water into the North Atlantic via the Greenland-Iceland-Scotland Ridge, and compensating northward flow of warm surface water. Physical models suggest that, in the absence of such overturning, oceanic heat transport to the Northern Hemisphere is reduced by as much as 50%, open North Atlantic sea-surface temperatures are as much as 6 degrees C lower, and the winter sea-ice limit migrates as far south as 45 degrees N. Although simulations of the equilibrium climate state for the Last Glacial Maximum (LGM) suggest the absence of GIN Seas overflow, tests of these model results have been hampered by ambiguity in sedimentary proxies. Here we present a bottom-water neodymium (Nd) isotope record from the Rockall Trough to investigate changes in the sources of circulating waters over the past 43 k.y. Today and throughout most of the Holocene, water from the GIN Seas, along with water from the North Atlantic Current (NAC) entrained during overflow, sets the bottom-water Nd isotope composition of the Rockall Trough to approximately -10. Our results suggest the persistence of this scenario back into the LGM and beyond to mid-Marine Isotope Stage 3. Periodic radiogenic excursions punctuate the record at times of meltwater events, implying either continued GIN Seas overflow without NAC entrainment, or millennial-scale interruptions in the overflow and shoaling of Southern Source Water. We conclude that overflow was at least intermittently present during the LGM, if not continuous, and that the GIN Seas have remained a source of deep water to the North Atlantic during the last glacial cycle.