We report the results of the highest-resolution teleseismic tomography study yet performed of the upper mantle beneath Iceland. The experiment used data gathered by the Iceland Hotspot Project, which operated a 35-station network of continuously recording, digital, broad-band seismometers over all of Iceland 1996-1998. The structure of the upper mantle was determined using the ACH damped least-squares method and involved 42 stations, 3159 P-wave, and 1338 S-wave arrival times, including the phases P, pP, sP, PP, SP, PcP, PKIKP, pPKIKP, S, sS, SS, SKS and Sdiff. Artefacts, both perceptual and parametric, were minimized by well-tested smoothing techniques involving layer thinning and offset-and-averaging. Resolution is good beneath most of Iceland from ??? 60 km depth to a maximum of ??? 450 km depth and beneath the Tjornes Fracture Zone and near-shore parts of the Reykjanes ridge. The results reveal a coherent, negative wave-speed anomaly with a diameter of 200-250 km and anomalies in P-wave speed, Vp, as strong as -2.7 per cent and in S-wave speed, Vs, as strong as -4.9 per cent. The anomaly extends from the surface to the limit of good resolution at ??? 450 km depth. In the upper ??? 250 km it is centred beneath the eastern part of the Middle Volcanic Zone, coincident with the centre of the ??? 100 mGal Bouguer gravity low over Iceland, and a lower crustal low-velocity zone identified by receiver functions. This is probably the true centre of the Iceland hotspot. In the upper ??? 200 km, the low-wave-speed body extends along the Reykjanes ridge but is sharply truncated beneath the Tjornes Fracture Zone. This suggests that material may flow unimpeded along the Reykjanes ridge from beneath Iceland but is blocked beneath the Tjornes Fracture Zone. The magnitudes of the Vp, Vs and Vp/Vs anomalies cannot be explained by elevated temperature alone, but favour a model of maximum temperature anomalies <200 K, along with up to ??? 2 per cent of partial melt in the depth range ??? 100-300 km beneath east-central Iceland. The anomalous body is approximately cylindrical in the top 250 km but tabular in shape at greater depth, elongated north-south and generally underlying the spreading plate boundary. Such a morphological change and its relationship to surface rift zones are predicted to occur in convective upwellings driven by basal heating, passive upwelling in response to plate separation and lateral temperature gradients. Although we cannot resolve structure deeper than ??? 450 km, and do not detect a bottom to the anomaly, these models suggest that it extends no deeper than the mantle transition zone. Such models thus suggest a shallow origin for the Iceland hotspot rather than a deep mantle plume, and imply that the hotspot has been located on the spreading ridge in the centre of the north Atlantic for its entire history, and is not fixed relative to other Atlantic hotspots. The results are consistent with recent, regional full-thickness mantle tomography and whole-mantle tomography images that show a strong, low-wave-speed anomaly beneath the Iceland region that is confined to the upper mantle and thus do not require a plume in the lower mantle. Seismic and geochemical observations that are interpreted as indicating a lower mantle, or core-mantle boundary origin for the North Atlantic Igneous Province and the Iceland hotspot should be re-examined to consider whether they are consistent with upper mantle processes.