We collected GPS data from the southern Tarim basin, the Qaidam basin, and the western Kunlun Shan region between 1993 and 1998 to determine crustal deformation along the Altyn Tagh fault system at the northern margin of the Tibetan plateau. We conclude from these data that the Altyn Tagh is a left-lateral strike slip fault with a current slip rate of ~9 mm/yr, in sharp contrast with geological estimates of 20--30 mm/yr. This contrast poses an enigma: because the GPS data cover a wider region than the geologic data, they might be expected to reveal somewhat more slip. We also find that the Tarim and Qaidam basins behave as rigid blocks within the uncertainty of our measurements, rotating clockwise at a rate of ~11 and ~4.5 nrad/yr, respectively, with respect to the Eurasia plate. The rotation of the Tarim basin causes convergence across the Tian Shan, increasing progressively westward from ~6 mm/yr at 87 ¿E to ~18 mm/yr at 77 ¿E. Our data and other GPS data suggest that the Indo-Asia collision is mainly accommodated by crustal shortening along the main Himalayan thrust system (~53%) and the Tian Shan contractional belt (~19%). Eastward extrusion of the Tibetan plateau along the Altyn Tagh and Kunlun faults accommodates only ~23% of the Indo-Asia convergence. ¿ 2001 American Geophysical Union