Observations of the H+3 infrared emission at 2 and 4 μm have suggested that H+3 is in local thermodynamic equilibrium (LTE) in the region of the Jovian ionosphere from which the emissions originate. We have tested this assumption by calculating the vibrational distribution of H3+ over the altitude range of 350 to 1500 km above the methane cloud tops (1 to 4¿10-3 μbar). We have constructed a model of the Jovian auroral ionosphere in which the neutral temperatures are enhanced over those of the mid-latitude ionosphere, as suggested by observations and models of the auroral region. We have modeled the precipitation of 10-keV electrons with an energy flux of 1 erg cm-2 s-1. Both the energy and energy flux are less than those that are implicated in the production of the UV aurora. We have computed the densities and vibrational distribution of H3+ and find that the distribution of the six lowest states of H3+ can be determined fairly well in spite of uncertainties in the atomic and molecular data. Since the nearly resonant transfer of vibration from H2(v=1) is an important process in populating the H3+(v1=0,v2=2) state,it is necessary to model the vibrational distribution of H2 as well. The computed altitude profiles and vibrational distributions of H3+ and H2 are consistent with the observations of infrared emission in the 2- and 4-μm regions. The H3+ is not in LTE near and above the H3+ peak, since loss of the H3+(v1=0,v2=1) and H3+(v1=0,v2=2) states by radiation is approximately equal to the collisional loss rate. ¿ American Geophysical Union 1992