We have inverted travel time data from seismic refraction profiles within the Snake River Plain, a volcanic-tectonic depression in southern Idaho, for crustal and uppermost mantle compressional velocity structure. The data in the vicinity of the youngest, northeastern volcanics in Yellowstone require the presence of a significant low velocity zone in the lower crust at depths between 20 and 40 km in order to explain the presence of a caustic at short ranges resulting from the crust-mantle transition. Data to the west are compatible with a model in which the velocity increases monotonically with depth. These observations are consistent with other data including the progressively lower crustal resistivity toward the northeast, the dated progression of volcanics from the southwest to the northeast at a rate of approximately 3.5 cm yr-1 and surface wave dispersion studies. The velocity reversals required by the data presented here and surface wave studies in the area are almost certainly related to elevated temperatures in the lower crust which approach or exceed the solidus of the deep crustal composition. The entire crustal section in the eastern Snake River Plain is characterized by very high velocities and can be represented by models with no first-order discontinuities with the possible exception of the Moho or crust-mantle transition.