Three teleseismic P-wave travel time data sets (KRISP 1985, 1989--1990; Kenya Broadband Seismic Experiment) have been inverted to obtain a new tomographic model of the upper mantle beneath the Kenya Rift. The model shows a 0.5--1.5% low velocity anomaly below the rift extending to about 150 km depth. Below ~150 km depth, the anomaly broadens to the west toward the Tanzania Craton, suggesting a westward dip to the structure. Tomographic images to the south in Tanzania and to the north in Ethiopia also show westward dipping low velocity anomalies below depths of ~150--200 km. The presence of westward dipping low velocity structures along much of the East African rift (Ethiopia, Kenya and Tanzania) is difficult to explain with a plume model and is consistent with some models of the African Superplume showing anomalous lower and upper mantle structure connecting at mid-mantle depths under the western side of East Africa.