Marine ice-sheet collapse can contribute to rapid sea-level rise. Today, the West Antarctic Ice Sheet contains an amount of ice equivalent to approximately six metres of sea-level rise, but most of the ice is in the slowly moving interior reservoir. A relatively small fraction of the ice sheet comprises several rapidly flowing ice streams which drain the ice to the sea. The evolution of this drainage system almost certainly governs the process of ice-sheet collapse. The thick and slow-moving interior ice reservoir is generally fixed to the underlying bedrock while the ice streams glide over lubricated beds at velocities of up to several hundred metres per year. The source of the basal lubricant — a water-saturated till overlain by a water system — may be linked to the underlying geology. The West Antarctic Ice Sheet rests over a geologically complex region characterized by thin crust, high heat flows, active volcanism and sedimentary basins. Here we use aerogeophysical measurements to constrain the geological setting of the onset of an active West Antarctic ice stream. The onset coincides with a sediment-filled basin incised by a steep-sided valley. This observation supports the suggestion that ice-stream dynamics — and therefore the response of the West Antarctice Ice Sheet to changes in climate — are strongly modulated by the underlying geology.