Eleven broadband digital seismic stations were deployed across the central Tibetan Plateau in the first extensive passive-source experiment attempted within the Tibetan Plateau. One year of recording resulted in 186 event-station pairs which we analyze to determine the characteristics of shear wave splitting in the upper mantle beneath the array. Measurements of the fast polarization direction and delay time for SKS and direct S arrivals reveal systematic variations along the north-south oriented array. In the north central region of the plateau, very large delay times are observed at three stations, the largest of which is BUDO with 2.4 s. However, at TUNL, which is off the northern edge of the plateau and 110 km from BUDO, and at sites in the south central plateau, splitting decreases by nearly a factor of 3. We also observe a systematic rotation of the fast azimuth from about 45 (NE) to 90 (E-W) from south to north along the array. A previously identified zone of inefficient Sn propagation correlates well with our region of large splitting observations. The large delay times suggest that a relatively high number of anisotropic crystals are preferentially alligned within the mantle-lid, beneath the north central portion of the Tibetan Plateau. In most cases, fast polarization directions appear to be parallel to surface geologic features suggesting as much as 200 km of the upper mantle has been involved in the collisional deformation that has produced the Tibetan Plateau.