We report on the discovery of a grounding-line sedimentary wedge ("till delta") deposited by Whillans Ice Stream, West Antarctica. Our observation is that grounding-line deposition serves to thicken the ice and stabilize the position of the grounding line. The ice thickness at the grounding line is greater than that of floating ice in hydrostatic equilibrium. Thus, the grounding line will tend to remain in the same location despite changes in sea level (until sea level rises enough to overcome the excess thickness that is due to the wedge). Further, our observation demonstrates the occurrence of rapid subglacial erosion, sediment transport by distributed subglacial till deformation, and grounding-line sedimentation, which have important implications for ice dynamics, numerical modeling of ice flow, and interpretation of the sedimentation record.