Seismic VP, VS, and VP/VS structure is imaged across the Yellowstone hot spot swell, including the hot spot track where magmatism occurred at the eastern Snake River Plain ~6--10 m.y. B.P. Data are teleseismic P and S travel time delays that have been corrected for the well-understood upper mantle anisotropy and crustal structure. Amplitude variations in the imaged structures are 6.2%, 11.2%, and 8% for VP, VS, and VP/VS, respectively. The dominant structure is a zone which extends beneath the Snake River Plain to a depth of ~190 km that is high in VP/VS and low in VP and VS. The physical state of the upper mantle is inferred by assuming isostasy, using the volume of melt segregated from the mantle that is inferred from estimates of magma addition to the crust, and using relations that scale changes in temperature, partial melt fraction and composition to density. Specifically, we infer that the low-velocity mantle beneath the Snake River Plain is partially molten up to 1.0%, and the high-velocity Yellowstone swell mantle away from the Snake River Plain is ~80¿ K cooler and ~5% depleted in basaltic component. The imaged large seismic velocity variations occur under near isothermal conditions.