Modern geodetic techniques, such as precise Global Positioning System (GPS) measurements and high resolution space gravity mapping, make it possible to measure the present-day rate of viscoelastic gravitational Earth response to present and past glacier mass change. Patagonia is a rapidly evolving glacial environment. Over the past decade, the local rate of surface stress unloading may be the largest anywhere on the planet. We compute the present-day land uplift rate that could be observed using bedrock GPS measurements. The Little Ice Age (LIA) of the past half millennium generates large vertical rates since the underlying mantle material is likely to have anomalously low viscosity owing to late-Neogene ridge subduction.