The Paleocene-Eocene Thermal Maximum (PETM, approximately 55 million years ago) was an interval of global warming and ocean acidification attributed to rapid release and oxidation of buried carbon. We show that the onset of the PETM coincided with a prominent increase in the origination and extinction of calcareous phytoplankton. Yet major perturbation of the surface-water saturation state across the PETM was not detrimental to the survival of most calcareous nannoplankton taxa and did not impart a calcification or ecological bias to the pattern of evolutionary turnover. Instead, the rate of environmental change appears to have driven turnover, preferentially affecting rare taxa living close to their viable limits.