We develop a three-dimensional viscoelastic finite element model to study postseismic deformation associated with the 1960 great Chile earthquake. GPS observations 35 years after the earthquake show that, while all coastal sites are moving landward, a group of inland sites 200--400 km from the trench are moving seaward and that coastal velocities in the 1960 rupture area are distinctly smaller than those to the north. We explain these observations in terms of mantle stress relaxation. The earthquake stretches the upper plate to move seaward, but elastic stresses coseismically induced in the upper mantle resist this motion. Stress relaxation allows seaward motion to take place in the inland area for several decades following the earthquake. With a viscosity of 2.5 ¿ 1019 Pa s for the continental upper mantle, the model well explains the GPS observations. Numerical tests suggest that the continental mantle viscosity value is reasonably well constrained. The model shows the prolonged postseismic seaward motion of the inland area to be a unique feature of earthquakes with very long rupture along strike and large coseismic fault slip. For short rupture and small coseismic slip, the motion will stop very quickly after the earthquake, explaining why this phenomenon is not more commonly observed. With an oceanic mantle viscosity of 1020 Pa s, the model also provides an explanation for tide-gauge constrained postseismic uplift 200 km from the trench that had previously been explained using a model of prolonged afterslip of a deep segment of the Chile subduction fault.