Current interest in nanophotonics has spurred the synthesis of a variety of molecular rotors--custom-designed molecules attached to a substrate via an axle about which the barrier to rotation is relatively low--and the investigation of their optical and mechanical properties. The dielectric response of molecular rotors possessing a permanent dipole moment, recently measured at frequencies in the kHz range, would be expected to be quite modest at optical frequencies. Nonpolar rotors, in contrast, could potentially exhibit large nonlinearities at optical frequencies, with the most promising rotor candidates being rigid molecules with molecular polarizabilities that are highly anisotropic; a good example is anthracene, for which the diagonal component of the polarizability tensor corresponding to the long axis of the molecule differs from that corresponding to axis normal to the ring plane by 20 Å3. Anthracene molecules are constrained to rotate about the principal axis associated with the diagonal component of the molecular polarizability that is intermediate in size. The rotation axes are oriented vertically ("azimuthal rotors") and are attached to a covalent monolayer grid such as that recently reported by Magnera et al. [in Nanostructural Materials: Clusters, Composites, and Thin Films, Moskovits and Shalaev, eds., ACS, 1997, p. 213]. In this configuration, the interaction between the incident laser beam and the induced rotor dipoles dominates the physics; rotor-rotor interactions are negligible. This allows us to calculate the nonlinear refractive index nI2 for the system, for which we obtain a relatively modest value of 2.6 × 10-15 cm2/W.