During the years 1981--1983, three intense seismic swarms took place in the Tahiti-Mehetia area of French Polynesia at the presumed location of the Society Island hot spot. The 1981 swarm featured 4000 earthquakes, with a maximum magnitude ML=4.3, in the immediate vicinity of the island of Mehetia; the 1982 swarm occurred along the flank of the major Teahitia seamount, and involved more than 9000 events; a second swarm occurred at Teahitia in 1983 and involved 3000 events. Although no precise constraint can be placed on the depth of individual events from their travel times to Polynesian stations, features in the evolution of the Mehetia swarm are generally consistent with the probable ascent of a magma body toward the surface. In the case of Teahitia, the recording of abundant tremors of both high and low frequency, particularly intense during the 1983 swarm, is directly similar to cases of documented volcanic eruptions. The swarms are interpreted as episodes of active volcanism, part of the process of building the next island in the chain.