In 1979, Voyager I provided the first strong evidence for the existence of lightning on another planet. Two pictures taken while the spacecraft was in Jupiter's shadow reveal about three dozen luminous spots on the night side of the planet. After careful examination of these spots, we conclude that they are lightning flashes occurring somewhere within Jupiter's atmosphere. A search through the additional Voyager I and II images of Jupiter's night hemisphere failed to locate any additional lightning flashes. The lower limit for the planetary lightning rate on Jupiter is found to be 10⁻⁴ km⁻² yr⁻¹. It must be noted that the spacecraft could only detect lightning discharges at least 1000 times higher than typical terrestrial flashes. Furthermore, due to attenuation, any discharges occurring deep within the atmosphere could not have been imaged. Calculations suggest that the actual flash rate could be about 0.1 km⁻² yr⁻¹. Analysis of the lightning images reveals that the flashes group near 50°N latitude. High-resolution photographs of the lightning region made in daylight about 65 hours before the discovery images show long, light ribbon-like clouds. Almost every flash appears to be associated with one of these clouds. Calculations made with a Monte Carlo radiative transfer code that computes the luminosity distribution of the spot on the top of the ammonia cloud that is produced by a point source within the atmosphere indicate that the lightning production region is near the top of the lower cloud deck. The average optical energy radiated by a discharge is calculated to be about 10⁹ J. The total electrical energy is estimated to be about 3 x 10¹² J. Calculations made with a chemical equilibrium model show that lightning synthesis cannot account for the observed abundances of such disequilibrium species as CO, HCN, and C₂H₂.