Changes in ice discharge from Antarctica constitute the largest uncertainty in future sea-level projections, mainly because of the unknown response of its marine basins. Most of West Antarctica's marine ice sheet lies on an inland-sloping bed and is thereby prone to a marine ice sheet instability. A similar topographic configuration is found in large parts of East Antarctica, which holds marine ice equivalent to 19 m of global sea-level rise, that is, more than five times that of West Antarctica. Within East Antarctica, the Wilkes Basin holds the largest volume of marine ice that is fully connected by subglacial troughs. This ice body was significantly reduced during the Pliocene epoch. Strong melting underneath adjacent ice shelves with similar bathymetry indicates the ice sheet's sensitivity to climatic perturbations. The stability of the Wilkes marine ice sheet has not been the subject of any comprehensive assessment of future sea level. Using recently improved topographic data in combination with ice-dynamic simulations, we show here that the removal of a specific coastal ice volume equivalent to less than 80 mm of global sea-level rise at the margin of the Wilkes Basin destabilizes the regional ice flow and leads to a self-sustained discharge of the entire basin and a global sea-level rise of 3-4 m. Our results are robust with respect to variation in ice parameters, forcing details and model resolution as well as increased surface mass balance, indicating that East Antarctica may become a large contributor to future sea-level rise on timescales beyond a century.