STROMBOLI volcano in the Aeolian islands has been erupting continuously for more than 2,000 years1, and probably as many as 5,000, following a major flank collapse2,3. Here we describe air-borne measurements of the plume flux of SO2 during 1980–93, which show that the volcano emits very large amounts of gas, mostly by open-conduit degassing between explosive outbursts, while exuding little basalt. Microprobe analysis of sulphur in the K-rich (shoshonitic) basalt, along with data for primitive basalts in the region4,5, suggests that the time-averaged SO2 flux is produced by intrusive degassing of 0.01-0.02 km3 yr-1 of magma, 100-200 times more than the volume erupted. Over 5,000 years, this rate implies that 50-100 km3 of intruded basalt would have been degassed, suggesting either that the volcanic pile has grown substantially by intrusion6 or, more probably, that a large magma storage system is emplaced at a shallow level within the crustal basement. Our results indicate that Etna and Stromboli alone provide 10% of the global budget of volcanic SO2.