Major ice sheets were permanently established on Antarctica approximately 34 million years ago, close to the Eocene/Oligocene boundary, at the same time as a permanent deepening of the calcite compensation depth in the world's oceans. Until recently, it was thought that Northern Hemisphere glaciation began much later, between 11 and 5 million years ago. This view has been challenged, however, by records of ice rafting at high northern latitudes during the Eocene epoch and by estimates of global ice volume that exceed the storage capacity of Antarctica at the same time as a temporary deepening of the calcite compensation depth approximately 41.6 million years ago. Here we test the hypothesis that large ice sheets were present in both hemispheres approximately 41.6 million years ago using marine sediment records of oxygen and carbon isotope values and of calcium carbonate content from the equatorial Atlantic Ocean. These records allow, at most, an ice budget that can easily be accommodated on Antarctica, indicating that large ice sheets were not present in the Northern Hemisphere. The records also reveal a brief interval shortly before the temporary deepening of the calcite compensation depth during which the calcite compensation depth shoaled, ocean temperatures increased and carbon isotope values decreased in the equatorial Atlantic. The nature of these changes around 41.6 million years ago implies common links, in terms of carbon cycling, with events at the Eocene/Oligocene boundary and with the 'hyperthermals' of the Early Eocene climate optimum. Our findings help to resolve the apparent discrepancy between the geological records of Northern Hemisphere glaciation and model results that indicate that the threshold for continental glaciation was crossed earlier in the Southern Hemisphere than in the Northern Hemisphere.