The Galileo spacecraft recently measured an ≈40% decrease of Jupiter's magnetic field near Io from a distance of 05 RIo [Kivelson et al., 1996>, a signature that cannot be explained in terms of the previously known Alfven wing current system alone. The Galileo observations can be explained by an additional magnetic moment of Io aligned with the ambient Jovian field. There is no Earth-like magnetosphere at Io because its magnetic moment is not sufficient to stand off the Jovian field far above Io's atmosphere. The Alfven wing current system must close within the Io interior, implying an electrical conductivity in the outer layers much higher than that expected for solid rock alone. Since widespread sulfur-rich aquifers are present to support Io's extensive volcanism, the thermal and electrical conductivities in Io's outer layers will be higher than would be the case for solid rock. We suggest that on average the temperature remains below the Curie point to a depth on the order of at least 300 km. Io's magnetic moment could then be explained as thermoremanent magnetization of ferromagnetic material. In this model, Io's outer layers cooled through the Curie temperature in a magnetic field about 15 times the current ambient field at Io. At that time, Io was closer to Jupiter, and/or Jupiter's dynamo magnetic moment was stronger. ¿ American Geophysical Union 1996