The hydrogenic ion composition and electrical conductivity are evaluated for the shallow interior of Jupiter extending from the 1-bar surface to a depth of 4000 km below this level. The atmosphere is assumed to be a mixture of hydrogen and helium with a standard mass density ratio of 78/22. The pressure and temperature are modeled assuming the gas is adiabatic, obeys the perfect gas law, and is in hydrostatic equilibrium. In this preliminary study the effects of impurities are ignored. The densities of free electrons, molecular and atomic hydrogen, and their positive and negative ions are computed assuming the atmosphere is in local thermodynamic equilibrium. From these quanteties are evaluated the electron- and ion-neutral collision frequencies and mobilities, and the electrical conductivity. Results of the calculation show that for a hydrogen/helium atmosphere electrical currents within the shallow interior of Jupiter are carried primarily by molecular hydrogen ions, but with nonnegligible contributions from electrons near the surface, and atomic hydrogen ions at greater depths. The electrical conductivity is sufficiently large to form a conducting “boundary” to electromagnetic waves propagating within the shallow interior. The location of this boundary is frequency dependent, ranging from a depth of 1000 km at 1 mHz to 3000 km at 1 MHz. The existence of a conducting boundary suggests that Jupiter possesses a closed planetary-ionosphere cavity similar to the earth-ionosphere cavity. Preliminary calculations yield eigenfrequencies of approximately 0.76, 1.35, and 1.93 Hz for the lowest three transverse-magnetic normal modes, respectively, with corresponding Q-factors of roughly 7. It is speculated that the normal modes of this system may be excited by Jovian lightning in a manner similar to the terrestrial Schumann resonances. Measurements of these modes could be used to diagnose the conductivity of the shallow interior.