The ice sheet in West Antarctica is grounded on a sub-sea level basin in the Antarctic continental shelf. At the seaward margins, where ice thicknesses are reduced sufficiently to attain neutral bouyancy, floating ice shelves form. The two largest are the Ross and Ronne ice shelves (Fig. 1). Because the depth of the continental shelf increases towards the centre of the West Antarctic ice sheet, ice discharge could accelerate irreversibly until the grounded portion of the ice sheet had completely disappeared1–3. The resistance to ice discharge provided by the ice shelves is the major factor preventing such a collapse4,5. Geological evidence indicates that the extent of grounded ice in the West Antarctic has fluctuated widely during the Pleistocene6,7, and complete removal of the ice sheet may have occurred during the Sangamon interglacial following a climatic warming which was probably associated with a retreat of the ice-shelf seaward margins8. One of the most active ice streams draining West Antarctica flows into the south-east corner of the Ross Ice Shelf. Surface observations in this area indicate that, either the ice shelf is thickening9, or that there is appreciable melting from beneath ice shelf that is >500 km from the open sea10. Such melting would strongly influence temperatures within the ice shelf, and here we use a temperature–depth profile from the ice shelf to estimate the basal regime. We conclude that, for much of the south-east corner, basal freezing/melting rates have been near zero for the past few hundred years. This implies that, within this region, the ice shelf is thickening at ∼0.3 m yr−1.