On 1999 September 21, the Mw 7.6 Chi-Chi earthquake ruptured a segment of the Chelungpu Fault, a frontal thrust fault of the Western Foothills of Taiwan. The stress perturbation induced by the rupture triggered a transient deformation across the island, which was well recorded by a wide network of continuously operating GPS stations. The analysis of more than ten years of these data reveals a heterogeneous pattern of postseismic displacements, with relaxation times varying by a factor of more than ten, and large cumulative displacements at great distances, in particular along the Longitudinal Valley in eastern Taiwan, where relaxation times are also longer. We show that while afterslip is the dominant relaxation process in the epicentral area, viscoelastic relaxation is needed to explain the pattern and time evolution of displacements at the larger scale. We model the spatiotemporal behavior of the transient deformation as the result of afterslip on the décollement that extends downdip of the Chelungpu thrust, and viscoelastic flow in the lower crust and in the mid-crust below the Central Range. We construct a model of deformation driven by coseismic stress change where afterslip and viscoelastic flow are fully coupled. The model is compatible with the shorter relaxation times observed in the near field, which are due to continued fault slip, and the longer characteristic relaxation times and the reversed polarity of vertical displacements observed east of the Central Range. Our preferred model shows a viscosity of 0.5-1×1019 Pas at lower-crustal depths and 5×10 17 Pas in the mid-crust below the Central Range, between 10 and 30km depth. The low-viscosity zone at mid-crustal depth below the Central Range coincides with a region of low seismicity where rapid advection of heat due to surface erosion coupled with underplating maintain high temperatures, estimated to be between 300°C and 600°C from the modeling of thermo-chronology and surface heat flow data.