Terrestrial cosmogenic nuclide concentrations of detrital minerals yield catchment-wide rates at which hillslopes erode. These estimates are commonly used to infer millennial scale denudation patterns and to identify the main controls on mass-balance and landscape evolution at orogenic scale. The same approach can be applied to minerals preserved in stratigraphic records of rivers, although extracting reliable paleo-denudation rates from Ma-old archives can be limited by the target nuclide's half-life and by exposure to cosmic radiations after deposition. Slowly eroding landscapes, however, are characterized by the highest cosmogenic radionuclide concentrations; a condition that potentially allows pushing the method's limits further back in time, provided that independent constraints on the geological evolution are available. Here, we report 13-10 million-year-old paleo-denudation rates from northernmost Chile, the oldest 10Be-inferred rates ever reported. We find that at 13-10 Ma the western Andean Altiplano has been eroding at 1-10 m/Ma, consistent with modern paces in the same setting, and it experienced a period with rates above 10 m/Ma at ~11 Ma. We suggest that the background tectono-geomorphic state of the western margin of the Altiplano has remained stable since the mid-Miocene, whereas intensified runoff since ~11 Ma might explain the transient increase in denudation.