Using Galileo clear-filter images (effective wavelength ≈0.64 μm), we have created the first albedo maps of the small inner jovian satellites Thebe, Amalthea, and Metis. These maps clearly show that the leading sides of all three satellites are significantly brighter than their corresponding trailing sides, confirming and extending a result first reported by P. C. Thomas et al. (1998, Icarus135, 360-371). In particular, on all three moons the leading side is brighter than the trailing side by 25 to 30%. The fact that the direction and size of this albedo asymmetry is identical from satellite to satellite suggests that one common physical mechanism is governing the global albedo patterns of all three moons. The most plausible such mechanism is the impact of macroscopic meteoroids that originated outside the jovian system. These impacts, which eject the dust that forms Jupiter's ring system (M. E. Ockert-Bell et al., 1999, Icarus138, 188-213; J. A. Burns et al., 1999, Science284, 1146-1150), are probably also responsible for brightening the leading sides of these small satellites.