Field-aligned currents, which are known to play an important role in the dynamics of the earth's magnetosphere, would also be expected to flow in the Jovian magnetosphere during magnetically active periods. Such currents are difficult to observe largely because of their limited spatial extent and intermittent nature, but on the Pioneer 11 inbound pass to Jupiter on day 336, 1800 GRT, near the L shell of Ganymede, the helium vector magnetometer recorded a structured perturbation with the characteristic signature of a field-aligned current. No analogous structure was found on a similar Pioneer 10 inbound pass (day 337, 1200 GRT). The perturbation could have been caused by turbulence within the wake of Ganymede through which the spacecraft was moving or the perturbation could represent the first observation of a Jovian substorm. The observations are discussed in terms of both models, and difficulties are examined.