A three-dimensional ray tracing program is used to investigate the propagation and dispersion of lightning-generated whistlers in the magnetosphere of Neptune. A simple empirical magnetospheric plasma model based on observational constraints is used for the plasma density distribution, and an offset tilted dipole model is used for the magnetic field. Source positions for the whistlers are chosen along magnetic field lines with L<3 in agreement with observations. Whistlers with frequencies of about 10 kHz generally propagate very near the resonance cone angle for most of the ray path, which produces dispersions considerably larger than those predicted for quasiparallel propagation. Dispersions computed using our ''standard'' plasma density model are over 30,000 s √Hz for ''one-hop'' whistlers which is comparable to observed values. In general, the whistlers were found to propagate about 10¿ in magnetic longitude during one hop and to cross L shells. These results strongly support the existence of whistlers at Neptune. The large dispersions are attributed to the large cold plasma population at Neptune which leads to propagation very near the resonance cone angle for a large part of the ray path. ¿American Geophysical Union 1991