The start of the Palaeocene/Eocene thermal maximum--a period of exceptional global warming about 55 million years ago--is marked by a prominent negative carbon isotope excursion that reflects a massive input of 13C-depleted ('light') carbon to the ocean-atmosphere system. It is often assumed that this carbon injection initiated the rapid increase in global surface temperatures and environmental change that characterize the climate perturbation, but the exact sequence of events remains uncertain. Here we present chemical and biotic records of environmental change across the Palaeocene/Eocene boundary from two sediment sections in New Jersey that have high sediment accumulation rates. We show that the onsets of environmental change (as recorded by the abundant occurrence ('acme') of the dinoflagellate cyst Apectodinium) and of surface-ocean warming (as evidenced by the palaeothermometer TEX86) preceded the light carbon injection by several thousand years. The onset of the Apectodinium acme also precedes the carbon isotope excursion in sections from the southwest Pacific Ocean and the North Sea, indicating that the early onset of environmental change was not confined to the New Jersey shelf. The lag of approximately 3,000 years between the onset of warming in New Jersey shelf waters and the carbon isotope excursion is consistent with the hypothesis that bottom water warming caused the injection of 13C-depleted carbon by triggering the dissociation of submarine methane hydrates, but the cause of the early warming remains uncertain.