Grounding line dynamics are key to our understanding of marine ice sheets such as the West Antarctic Ice Sheet (WAIS). We present an accurate and rapid method for locating grounding lines using GLAS ICESat laser altimetry data. We then apply this technique to the Siple Coast region of the WAIS. Our technique exploits the high surface slope at the grounding line relative to the adjacent flat ice streams and ice shelf. The technique is validated by ground-based observations. Comparisons between the current grounding line and earlier measured locations demonstrate that the Siple Coast's grounding line has been largely static over the last two decades. This is important as the ice streams have been undergoing considerable variations over this period. We conclude that ice stream flow speeds can vary while the grounding line remains stable. We suggest that grounding lines may migrate abruptly and then stabilize rather than undergoing continuous retreat.