ON 27 June 1996 the Galileo spacecraft(1,2) made the first of four planned close fly-bys of Ganymede, Jupiter’s largest moon, Here we report measurements of plasma waves and radio emissions, over the frequency range 5 Hz to 5.6 MHz during the first encounter, Intense plasma waves were detected over a region of space nearly four times Ganymede’s diameter, which is much larger than would be expected for a simple wake arising from Ganymede’s passage through Jupiter’s rapidly rotating magnetosphere. The types of waves detected (whistler-mode emissions, upper hybrid waves, electrostatic electron cyclotron waves and escaping radio emission) strongly suggest that Ganymede has a large, extended magnetosphere of its own, The data indicate the presence of a strong (B > 400 nT) magnetic field, and show that Ganymede is surrounded by an ionosphere-like plasma with a maximum electron density of about 100 particles cm(-3) and a scale height of about 1,000 km.