The relationship between the rise of the Andean mountain chain and the onset of aridity on its western margin is poorly understood. Canyon incision on both the eastern and western flanks of the chain is interpreted generally as a direct response to increased rock uplift, but may equally have been the result of climate change. Here we record some of the oldest canyon incision on the western Andean margin by tracking the downward migration of the local water table using (U-Th)/He hematite geochronology on vertical drill-core transects. Our data constrain the incision history of the Quebrada de Parca canyon in northern Chile from ca. 16 Ma to the present day. The erosional and topographic response of the Quebrada de Parca river suggests that incision was induced by a switch to a more arid climate in the middle Miocene, which reduced regional precipitation and river discharge. Geomorphic analysis of the modern river suggests that the Central Andes have gained only ∼700 m of elevation since incision began, and had therefore reached at least 50% of their current elevation by middle Miocene time. We thus conclude that the onset of aridity at ca. 16 Ma occurred subsequent to the main Andean uplift.