The Earth's climate abruptly warmed by 5-8 °C during the Palaeocene-Eocene thermal maximum (PETM), about 55.5 million years ago. This warming was associated with a massive addition of carbon to the ocean-atmosphere system, but estimates of the Earth system response to this perturbation are complicated by widely varying estimates of the duration of carbon release, which range from less than a year to tens of thousands of years. In addition the source of the carbon, and whether it was released as a single injection or in several pulses, remains the subject of debate. Here we present a new high-resolution carbon isotope record from terrestrial deposits in the Bighorn Basin (Wyoming, USA) spanning the PETM, and interpret the record using a carbon-cycle box model of the ocean-atmosphere-biosphere system. Our record shows that the beginning of the PETM is characterized by not one but two distinct carbon release events, separated by a recovery to background values. To reproduce this pattern, our model requires two discrete pulses of carbon released directly to the atmosphere, at average rates exceeding 0.9 Pg C yr-1, with the first pulse lasting fewer than 2,000 years. We thus conclude that the PETM involved one or more reservoirs capable of repeated, catastrophic carbon release, and that rates of carbon release during the PETM were more similar to those associated with modern anthropogenic emissions than previously suggested.