Teleseismic shear wave splitting measured at 56 continuous and temporary seismographs deployed in a 500 km by 600 km area around the Yellowstone hot spot indicates that fast anisotropy in the mantle is parallel to the direction of plate motion under most of the array. The average split time from all stations of 0.9 s is typical of continental stations. There is little evidence for plume-induced radial strain, suggesting that any contribution of gravitationally spreading plume material is undetectably small with respect to the plate motion velocity. Two stations within Yellowstone have splitting measurements indicating the apparent fast anisotropy direction ($phi$) is nearly perpendicular to plate motion. These stations are ~30 km from stations with $phi$ parallel to plate motion. The 70¿ rotation over 30 km suggests a shallow source of anisotropy; however, split times for these stations are more than 2 s. We suggest melt-filled, stress-oriented cracks in the lithosphere are responsible for the anomalous $phi$ orientations within Yellowstone. Stations southeast of Yellowstone have measurements of $phi$ oriented NNW to WNW at high angles to the plate motion direction. The Archean lithosphere beneath these stations may have significant anisotropy capable of producing the observed splitting.