An eyewitness sees ball lightning as a luminous sphere in regions of thunderstorm activity. There are many reports of ball lightning forming after a lightning discharge, existing for several seconds, and terminating suddenly and silently, or exploding with or without material damage1,2. Jennison3 has described ball lightning observed at close range inside a commercial aircraft shortly after a lightning discharge. As it drifted down the aisle of the passenger cabin, this ball lightning exhibited: (1) perfect equilibrium in a perfectly spherical shape with diameter 22+/-2 cm; (2) 5-10 W of optical radiation in blue-white light, but no heat radiation; and (3) an optically thick surface of almost solid appearance, devoid of polar or toroidal structure, but with some limb-darkening. It seems unreasonable to dismiss Jennison's ball lightning as an optical illusion4 (afterimage of the eye's retina). A physical explanation in terms of a microwave cavity5, a d.c. glow discharge6, chemical reactions7, nuclear reactions8 or annihilation of antimatter9 runs into difficulties since the all-metal airplane structure would act effectively as an air-tight Faraday cage. A plethora of excited atoms and molecules, and electromagnetic waves ranging from radio frequencies to X rays are produced in the channel of a lightning discharge, but only electric charge itself can enter the interior of an all-metal airplane without difficulty. Here a new model is presented which explains ball lightning in terms of electric charge.