Muon spin relaxation has been used to probe the charge carrier motion in the molecular conductor Alq₃ (tris[8-hydroxy-quinoline] aluminum). At 290 K, the magnetic field dependence of the muon spin relaxation corresponds to that expected for highly anisotropic intermolecular electron hopping. Intermolecular mobility in the fast hopping direction has been found to be 0.23±0.03  cm² V⁻¹ s⁻¹ in the absence of an electric- field gradient, increasing to 0.32±0.06  cm² V⁻¹ s⁻¹ in an electric field gradient of 1  MV m⁻¹. These intrinsic mobility values provide an estimate of the upper limit for mobility achievable in bulk material.