Earthquakes are accompanied by coseismic and post-seismic rebound: blocks of crust on either side of the fault spring back to their initial, undeformed configuration. This rebound is well documented by space geodetic data, such as the Global Positioning System. Thus, all earthquake-induced deformation of the crust is considered non-permanent and is modelled as an elastic or visco-elastic process. Here, however, we show that earthquakes larger than magnitude 7 in northern Chile caused the crust to deform permanently. We identify millimetre- to metre-scale tension cracks in the crust of the Atacama Desert and use cosmogenic nuclides to date the timing of crack formation. The cracks were formed by between 2,000 and 9,000 individual plate-boundary earthquakes that occurred in the past 0.8–1 million years. We show that up to 10% of the horizontal deformation generated during the earthquakes, recorded by Global Positioning System data and previously assumed to be recoverable, is permanent. Our data set provides a record of permanent strain in the shallow crust of the South American Plate. Although deformation of the deep crust may be predominantly elastic, we conclude that modelling of the earthquake cycle should also include a significant plastic component.