A GPS station in Manaus, near the center of the Amazon basin, manifests an annual cycle of vertical displacement with a peak-to-peak amplitude of 50--75 mm. This is by far the largest crustal oscillation observed to date, and nearly 2--3 times larger than the amplitude predicted for this region. Vertical ground displacement is strongly anti-correlated with the local stage height of the Amazon river, with no detectable time lag between the two time series. This suggests that we are observing, for the first time, a purely elastic response to changes in the weight of a flowing river system. We use a simple hydrological model to relate stage height to the regional pattern of flooding, and argue that the elastic oscillations observed in Manaus are dominated by changes in water loading developed within ~200 km of the GPS station.