THE Galileo spacecraft has now passed close to Jupiter’s largest moon-Ganymede-on two occasions, the first at an altitude of 838 km, and the second at an altitude of just 264 km. Here we report the discovery during these encounters of an internal magnetic field associated with Ganymede (the only other solid bodies in the Solar System known to have magnetic fields are Mercury, Earth and probably Io(1)), The data are consistent with a Ganymede-centred magnetic dipole tilted by similar to 10 degrees relative to the spin axis, and an equatorial surface-field strength of similar to 750 nT, The magnetic field is strong enough to carve out a magnetosphere with clearly defined boundaries within Jupiter’s magnetosphere, Although the observations require an internal field, they do not indicate its source. But the existence of an internal magnetic field should in itself help constrain models of Ganymede’s interior.