Recent observations from the Galileo spacecraft suggest that Io, the innermost of Jupiter's satellites, has a magnetic signature. Remanent magnetization appears inadequate to explain this signal and, given the huge tidal heating of Io's mantle, a convectively-stirred molten core seems unlikely. Instead, we propose that Io's magnetic field may be a direct consequence of hydromagnetic instabilities driven in its molten core by Jupiter's tides. Laboratory realisations of such 'tidal' instabilities confirm their potency as a means for extreme 'stirring' and dissipation. The energy to sustain Io's magnetic field would then come ultimately from Jupiter's rotational energy rather than an internal source as currently favoured in the Earth's case. ¿ 1998 American Geophysical Union