The Galileo spacecraft passed behind Jupiter on December 8, 1995, allowing the first radio occultation measurements of its ionospheric structure in 16 years. At ingress (24 ¿S, 68 ¿W), the principal peak of electron density is located at an altitude of 900 km above the 1-bar pressure level, with a peak density of 105 cm-3 and a thickness of ~200 km. At egress (43 ¿S, 28 ¿W), the main peak is centered near 2000 km altitude, with a peak density of 2¿104 cm-3 and a thickness of ~1000 km. Two thin layers, possibly forced by upwardly propagating gravity waves, appear at lower altitudes in the ingress profile. This is the first in a two-year series of observations that should help to resolve long-standing questions about Jupiter's ionosphere.¿ 1997 American Geophysical Union