We have analyzed 5 years of continuous Global Positioning System (GPS) measurements taken at Kellyville, just off the western margin of the ice sheet in southern Greenland. A fit to the vertical component gives a negative secular uplift rate of −5.8±1.0 mm/yr. A negative rate (i.e., a subsidence) is consistent with archeological and historical evidence that the surrounding region has been subsiding over the last 3 kyr. However, it is inconsistent with estimates of the Earth's continuing viscoelastic response to melting ice prior to 4 ka years ago, which predict that Kellyville should be uplifting, rather than subsiding, by 2.0±3.5 mm/yr. The resulting −7.8±3.6 mm/yr discrepancy is too large to be the result of loading from present‐day changes in nearby ice. We show, instead, that it is consistent with independent suggestions that the western ice sheet margin in this region of Greenland may have advanced by ≈50 km during the past 3–4 kyr.