The Antarctic Ice Sheet stores water equivalent to 58 m in global sea-level rise. We show in simulations using the Parallel Ice Sheet Model that burning the currently attainable fossil fuel resources is sufficient to eliminate the ice sheet. With cumulative fossil fuel emissions of 10,000 gigatonnes of carbon (GtC), Antarctica is projected to become almost ice-free with an average contribution to sea-level rise exceeding 3 m per century during the first millennium.