During the Voyager 2 flyby of Neptune, a series of 16 whistler-like events were detected by the plasma wave instrument near closest approach. These events were observed at radial distances from 1.30 to 1.99 R sub N and magnetic latitudes from -7 to 33 deg. The frequencies ranged from 6.1 to 12.0 kHz, and the dispersions fit the Eckersley law for lightning-generated whistlers. Lightning in the atmosphere of Neptune is the only known source of such signals. The frequency range of the whistlers (up to 12 kHz) indicates that the local electron densities are substantially higher (N sub e greater than 30 to 100 per cu cm) than indicated by the in situ plasma measurements. The dispersion of the whistlers is very large, typically 26,000 sec Hz(exp 0.5). Based on existing plasma density models and measurements, the dispersions are too large to be accounted for by a single direct path from the lightning source to the spacecraft. Therefore, multiple bounces from one hemisphere to the other are required. The most likely propagation path probably involves a lightning source on the dayside of the planet, with repeated bounces through the dense dayside ionosphere at low L-values.