A 200,000-yr interval of extreme global warming marked the start of the Eocene epoch about 55 million years ago. Negative carbon- and oxygen-isotope excursions in marine and terrestrial sediments show that this event was linked to a massive and rapid (approximately 10,000 yr) input of isotopically depleted carbon. It has been suggested previously that extensive melting of gas hydrates buried in marine sediments may represent the carbon source and has caused the global climate change. Large-scale hydrate melting, however, requires a hitherto unknown triggering mechanism. Here we present evidence for the presence of thousands of hydrothermal vent complexes identified on seismic reflection profiles from the Vøring and Møre basins in the Norwegian Sea. We propose that intrusion of voluminous mantle-derived melts in carbon-rich sedimentary strata in the northeast Atlantic may have caused an explosive release of methane--transported to the ocean or atmosphere through the vent complexes--close to the Palaeocene/Eocene boundary. Similar volcanic and metamorphic processes may explain climate events associated with other large igneous provinces such as the Siberian Traps (approximately 250 million years ago) and the Karoo Igneous Province (approximately 183 million years ago).