We present the Jovian Ionospheric Model (JIM), a time-dependent, three-dimensional model for the thermosphere and ionosphere of Jupiter. We describe the physical inputs for the hydrodynamic, thermodynamic and chemical components of the model, which is based on the UCL Thermosphere Model of Fuller-Rowell and Rees <1980>. We then present the results of an illustrative simulation in which an initially neutral homogeneous planet evolves for approximately 4 Jovian rotations, under the influence of solar illumination and auroral (electron) precipitation at high latitudes. The model shows that solar zenith angle, auroral activity, ion recombination chemistry and, to a lesser degree, magnetic field orientation, all play a role in forming the dayside and nightside global ionization patterns. We compare auroral and nonauroral/equatorial ionospheric compositions and find the signature of ion transport by fast winds. We also include a localized spot of precipitation in our model and comment on the associated ionization signatures which develop in response to this Io-like aurora. The simulation also develops strong outflows with velocities up to ~600 m s-1 from the auroral regions, driven mainly by pressure gradients. These pressure gradients, in turn, arise from the differences in chemical composition between the auroral and nonauroral upper thermospheres, as evolution proceeds. This preliminary study indicates a strong potential for JIM in analysis of two-dimensional image data and simulation of time-dependent global events. ¿ 1998 American Geophysical Union