We describe the detection of teleseismic surface waves from the 3 November 2002 Mw 7.9 Denali fault earthquake in Alaska with a dense network of 1 Hz GPS stations in southern California, about 3900 km from the event. Relative horizontal displacements with amplitudes in excess of 15 mm and duration of 700 seconds agree with integrated velocities recorded by nearby broadband seismometers with an rms difference of 2--3 mm. The displacements are derived from independent 1 Hz instantaneous positions demonstrating that a GPS network can provide direct measurements of arbitrarily large dynamic and static ground horizontal displacements at periods longer than 1 s and amplitudes above 2 mm, with an inherent precision (signal to noise) that improves indefinitely with amplitude without clipping and in real time. High-rate, real-time GPS networks can enhance earthquake detection and seismic risk mitigation and support other applications such as intelligent transportation and civil infrastructure monitoring.