Starting early in 2005, the positions of GPS stations in the San Gabriel valley region of southern California showed statistically significant departures from their previous behavior. Station LONG moved up by about 47 mm, and nearby stations moved away from LONG by about 10 mm. These changes began during an extremely rainy season in southern California and coincided with a 16-m increase in water level at a nearby well in Baldwin Park and a regional uplift detected by interferometric synthetic aperture radar. No equivalent signals were seen in GPS station position time series elsewhere in southern California. Our preferred explanation, supported by the timing and by a hydrologic simulation, is deformation due to recharging of aquifers after near-record rainfall in 2004--2005. We cannot rule out an aseismic slip event, but we consider such an event unlikely because it requires slip on multiple faults and predicts other signals that are not observed.