Electrostatic discharges in planetary atmospheres appear to be common throughout the Solar System, occurring on Earth, Jupiter, Saturn, Uranus, and possibly Venus and Neptune. Lightning is generally caused by the separation of electric charge on precipitating particles and therefore requires the presence of condensed cloud layers. Neptune has several cloud layers, including a high-altitude methane cloud, a H2S–NH3 layer, and deeper layers of water and ammonium hydrosulfide (NH4SH). Neptune appears to be a good candidate for lightning and other dynamic atmospheric phenomena because of its large internal heat source. Despite the presence of radio-frequency whistlers often associated with lightning, lightning has never been optically detected on Neptune. This may indicate that lightning is occurring too deep in the atmosphere to be seen at visible wavelengths. We investigate the possibility of lightning on Neptune using a particle-growth and charge-separation model that has previously been successfully applied to the Earth and Jupiter. We find that lightning is inhibited in the deep water or NH4SH cloud because of the high atmospheric pressures there; lightning seems possible in the H2S–NH3 cloud provided that transfer of charge can occur at a rate not less than 1% of that seen in water ice collisions.