Lightning is a familiar feature of storms on the Earth, and has also been seen on Jupiter and inferred indirectly to occur on Venus and Neptune. On Jupiter, lightning may be important as a source of energy to drive chemical reactions in the atmosphere, perhaps determining the abundances of molecules such as CO, HCN and C2H2. Lightning may be generated in Jupiter's water clouds by a mechanism similar to that which operates in terrestrial thunderstorms. Here we investigate the development of lightning by modelling the thunderstorm separation of electrical charge on precipitating ice particles at varying depths in Jupiter's atmosphere. We find that lightning can indeed be generated in the jovian water clouds, and that--in agreement with estimates from the analysis of Voyager images--it is most likely to occur at the 3- or 4-bar pressure level. Our model also predicts that a condensed-water abundance in the range of at least 1-2 g m-3 is required for lightning to occur in jovian thunderstorms--a prediction that may be tested when the Galileo probe arrives at Jupiter on 7 December 1995.