In 1993 June and July, we obtained 18 spectra of Jupiter's aurora in the wavelength range 1586-1620 Å using the Goddard High Resolution Spectrograph on board the Hubble Space Telescope (HST). The field of view for each observation was 2" × 2". There were 14 spectra of the northern and four spectra of the southern auroral ovals. The spectra are dominated by vibrational-rotational lines of the H2 Lyman band system, from which we have determined H2 rotational temperatures which correspond to the altitude region where most of the auroral emission originates. Intense emission was observed in two spectra at longitude 155°-165°, latitude 50° 65°, at a time when the central meridian longitude was near 190°. This location coincides with a bright spot in HST Faint Object Camera images of Jupiter's northern aurora. We estimate total emission rates in the Lyman band system of ~250 kR for the bright regions and ~25-130 kR for the fainter regions. The best-fit temperatures for the bright region and fainter regions are in the ranges 200-500 K and 200-800 K, respectively. The relatively low temperatures for the bright regions may indicate that the precipitating primary particles responsible for UV emission there penetrate more deeply than do particles in the fainter regions, to altitudes where the temperatures are lower because of efficient cooling by hydrocarbons.