This proposal is to use the Short Wavelength Spectrometer to detect the forbidden pure rotational spectrum of the H3+ molecular ion in the ionosphere of Jupiter. A detection of three or more lines, will: 1) Be the first ever detection of this fundamental spectrum; 2) Answer important questions about the concentration of H3+ in the jovian aurorae, and the physical conditions which prevail there. The H3+ ground state rotational spectrum covers the 10-40 micron region which is difficult to observe from the ground, but which is readily accessible to ISO's SWS. proposed to use the SWS in Fabry-Perot line scanning mode, to carry out the accurate measurements necessary to identify this spectrum. Several lines are need to compute the relevant temperature and column density.