It is commonly thought that the longer the time since last earthquake, the larger the next earthquake's slip will be. But this logical predictor of earthquake size, unsuccessful for large earthquakes on a strike-slip fault, fails also with the giant 1960 Chile earthquake of magnitude 9.5 (ref. 3). Although the time since the preceding earthquake spanned 123 years (refs 4, 5), the estimated slip in 1960, which occurred on a fault between the Nazca and South American tectonic plates, equalled 250-350 years' worth of the plate motion. Thus the average interval between such giant earthquakes on this fault should span several centuries. Here we present evidence that such long intervals were indeed typical of the last two millennia. We use buried soils and sand layers as records of tectonic subsidence and tsunami inundation at an estuary midway along the 1960 rupture. In these records, the 1960 earthquake ended a recurrence interval that had begun almost four centuries before, with an earthquake documented by Spanish conquistadors in 1575. Two later earthquakes, in 1737 and 1837, produced little if any subsidence or tsunami at the estuary and they therefore probably left the fault partly loaded with accumulated plate motion that the 1960 earthquake then expended.

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Individual great earthquakes are posited to release the elastic strain energy that has accumulated over centuries by the gradual movement of tectonic plates 1,2 . However, knowledge of plate deformation during a complete seismic cycle-two successive great earthquakes and the intervening interseismic period-remains incomplete 3 . A complete seismic cycle began in south-central Chile in 1835 with an earthquake of about magnitude 8.5 (refs 4,5) and ended in 2010 with a magnitude 8.8 earthquake 6 . During the first earthquake, an uplift of Isla Santa María by 2.4 to 3 m was documented 4,5 . In the second earthquake, the island was uplifted 7 by 1.8 m. Here we use nautical surveys made in 1804, after the earthquake in 1835 and in 1886, together with modern echo sounder surveys and GPS measurements made immediately before and after the 2010 earthquake, to quantify vertical deformation through the complete seismic cycle. We find that in the period between the two earthquakes, Isla Santa María subsided by about 1.4 m. We simulate the patterns of vertical deformation with a finite-element model and find that they agree broadly with predictions from elastic rebound theory 2 . However, comparison with geomorphic and geologic records of millennial coastline emergence 8,9 reveal that 10