The Gulf Stream is an ocean current that modulates climate in the Northern Hemisphere by transporting warm waters from the Gulf of Mexico into the North Atlantic and Arctic oceans. A changing Gulf Stream has the potential to thaw and convert hundreds of gigatonnes of frozen methane hydrate trapped below the sea floor into methane gas, increasing the risk of slope failure and methane release. How the Gulf Stream changes with time and what effect these changes have on methane hydrate stability is unclear. Here, using seismic data combined with thermal models, we show that recent changes in intermediate-depth ocean temperature associated with the Gulf Stream are rapidly destabilizing methane hydrate along a broad swathe of the North American margin. The area of active hydrate destabilization covers at least 10,000 square kilometres of the United States eastern margin, and occurs in a region prone to kilometre-scale slope failures. Previous hypothetical studies postulated that an increase of five degrees Celsius in intermediate-depth ocean temperatures could release enough methane to explain extreme global warming events like the Palaeocene-Eocene thermal maximum (PETM) and trigger widespread ocean acidification. Our analysis suggests that changes in Gulf Stream flow or temperature within the past 5,000 years or so are warming the western North Atlantic margin by up to eight degrees Celsius and are now triggering the destabilization of 2.5 gigatonnes of methane hydrate (about 0.2 per cent of that required to cause the PETM). This destabilization extends along hundreds of kilometres of the margin and may continue for centuries. It is unlikely that the western North Atlantic margin is the only area experiencing changing ocean currents; our estimate of 2.5 gigatonnes of destabilizing methane hydrate may therefore represent only a fraction of the methane hydrate currently destabilizing globally. The transport from ocean to atmosphere of any methane released--and thus its impact on climate--remains uncertain.