Internal isochronous ice sheet layers, recorded by airborne ice-penetrating radar, were measured along an ice flowline across a large (> I km high) subglacial hill in the foreground of the Transantarctic Mountains. The layers, dated through an existing stratigraphic link with the Vostok ice core, converge with the ice surface as ice flows over the hill without noticeable change to their separation with each other or the ice base. A two-dimensional ice flow model that calculates isochrons and particle flowpaths and accounts for ice flow over the hill under steady-state conditions requires net ablation (via sublimation) over the stoss face for the predicted isochrons to match the measured internal layers. Satellite remote sensing data show no sign of exposed ancient ice at this site, however. Given the lack of exposed glacial ice, surface balance conditions must have changed recently from the net ablation that is predicted at this site for the last 85,000 years to accumulation.