Teleseismic P wave arrival times recorded by a dense network of seismograph stations located on Kilauea volcano, Hawaii, are inverted to determine lateral variation in crust and upper mantle structure to a depth of 70 km. The crustal structure is dominated by relatively high velocities within the central summit complex and along the two radial rift zones compared with the nonrift flank of the volcano. Both the mean crustal velocity contrast between summit and nonrift flank and the distribution of velocities agree well with results from crustal refraction studies. Comparison of the velocity structure with Bouguer gravity anomalies over the volcano through a simple physical model also gives excellent agreement. Mantle structure appears to be more homogeneous than crustal structure. The root mean square velocity variation for the mantle averages only 1.5%, whereas variation within the crust exceeds 4%. The summit of Kilauea is underlain by normal velocity (8.1 km/s) material within the uppermost mantle (12--25 km), suggesting that large magma storage reservoirs are not present at this level and that the passageways from deeper sources must be quite narrow. No evidence is found for substantial volumes of partially molten rock (5%) within the mantle to depths of at least 40 km. Below about 30 km, low-velocity zones (1--2%) underlie the summits of Kilauea and nearby Mauna Loa and extend south of Kilauea into a broad offshore zone. Correlation of volcanic tremor source locations and persistent zones of mantle earthquakes with low-velocity mantle between 27.5- and 42.5-km depth suggests that a laterally extensive conduit system feeds magma to the volcanic summits from sources either at comparable depth or deeper within the mantle. The center of contemporary magmatic production and/or upwelling from deeper in the mantle appears to extend well to the south of the active volcanic summits, suggesting that the Hawaiian Island chain is actively extending to the southeast.