The 14 November 2001, Mw = 7.8, Kokoxili earthquake ruptured more than 400 km of the westernmost stretch of the left-lateral Kunlun fault in northern Tibet. Interferometric synthetic aperture radar data from descending orbits, along four adjacent tracks covering almost the entire rupture, and 1-m pixel Ikonos satellite images are used to map the rupture geometry and the surface displacements produced by the event. Interferograms are then inverted to solve for coseismic slip on the fault at depth. The radar data show that the rupture connected the Heituo fault, where the earthquake initiated, to the main Kunlun fault, cutting across a pull-apart trough in between the two strike-slip faults. The fault model includes two vertical sections extending to a depth of 20 km and discretized into 5 km ¿ 5 km patches. Using a nonnegative least squares method that includes an appropriate degree of smoothing, we solve for the left-lateral slip on each fault patch. Our solution shows that the largest slip occurred at depths between 0 and 5 km, reaching $simeq$8 m in two areas, 200 and 250 km east of the earthquake epicenter. Significant slip took place below 10 km at both ends of the rupture. Slip appears to have been highly variable along the fault, defining six sections of major moment release. These sections correspond to six subsegments of the Kunlun fault system, defined from the surface morphology of the fault. This suggests that fault geometry exerted a predominant influence on controlling the rupture propagation.