It has long been recognized that the properties of the Cook-Austral chain (Fig. 1) of volcanoes in the South Pacific are difficult to reconcile with the theory that volcanic activity in plate interiors is produced by the drift of tectonic plates over narrow, stationary plumes(1) of hot mantle material upwelling from depth. Radiometric dates(2,3) from many island samples are younger or older than would be predicted if a single plume currently located at volcanically active Macdonald seamount(4) was responsible for all of the volcanoes. Indeed, only the southernmost part of the Austral volcanic line has hitherto appeared to be consistent with plume activity, and then only within the past 6 million years (Myr)(5,6). Here we report radiometric dates that demonstrate that these southern Austral volcanoes are actually composed of three distinct volcanic chains with a range of ages spanning 34 Myr and with inconsistent age progressions. Gravity anomalies and seafloor fabric suggest that the volume and location of volcanism in this region is controlled by stress in the lithosphere rather than the locus of narrow plumes rising from the deep Earth.