Along the western margin of South America, plate convergence is accommodated by slip on the subduction interface and deformation of the overriding continent. In Chile, Bolivia, Ecuador and Colombia, continental deformation occurs mostly through the motion of discrete domains, hundreds to thousands of kilometres in scale. These continental slivers are wedged between the Nazca and stable South American plates. Here we use geodetic data to identify another large continental sliver in Peru that is about 300-400 km wide and 1,500 km long, which we call the Inca Sliver. We show that movement of the slivers parallel to the subduction trench is controlled by the obliquity of plate convergence and is linked to prominent features of the Andes Mountains. For example, the Altiplano is located at the boundary of converging slivers at the concave bend of the central Andes, and the extending Gulf of Guayaquil is located at the boundary of diverging slivers at the convex bend of the northern Andes. Motion of a few large continental slivers therefore controls the present-day deformation of nearly the entire Andes mountain range. We also show that a 1,000-km-long section of the plate interface in northern Peru and southern Ecuador slips predominantly aseismically, a behaviour that contrasts with the highly seismic neighbouring segments. The primary characteristics of this low-coupled segment are shared by â ̂1/420% of the subduction zones in the eastern Pacific Rim. © 2014 Macmillan Publishers Limited. All rights reserved.