Sixteen 3-component, 5-sec stations along a profile crossing the Altyn Tagh fault (ATF) at ~90 ¿E were used to measure shear wave splitting beneath Tibet's northern edge. Splitting delay times (Δt) of 0.3 to 1.3 sec show a marked increase in a narrow zone centered on the fault, implying anisotropy in the lithospheric mantle. Fast Polarization Directions (FPD) (ϕ) swing counterclockwise, from a mean azimuth of ~110 ¿E in the Qaidam basin south of the fault, to a mean azimuth of ~60 ¿E in the Altyn mountains. This swing occurs in less than 40 km. Both the Δt increase and FPD swing are consistent with ductile sinistral shear along the 40 km-wide, low P-wave velocity anomaly (-6--8%) imaged to a depth of ~140 km beneath the fault by teleseismic tomography. This confirms that the ATF guides the northeastwards extrusion of the Tibet-Qaidam's lithosphere relative to the Tarim's. ¿ 1999 American Geophysical Union