We have investigated NO production in the expansion phase of a lightning discharge using a hydrodynamic model coupled with the chemical rate equations for the two Zel'dovich reactions and oxygen dissociation. We have found that most of the NO production occurs early in the discharge, prior to shock wave formation, and that the rapid drop in density, not temperature, controls NO formation. The number of molecules per Joule (P) depends strongly on the energy per unit volume in the initial heated channel: this dependence is nonlinear with a maximum value of 26¿1016 molecules NO/J. For a representative discharge at a pressure of 1 atm, the number produced is 15¿1016/J. Initial investigation indicates that for a constant energy density (estimated to be about 6 MJ/m3) the rate of production drops off rapidly with decreasing air density and thus altitude. Use of P appropriate for sea level pressure may lead to a major overestimate of the rate of NO formation in atmospheric lightning, much of which occurs at high altitude. We present suggestions for new laboratory experiments to quantify global NO production by lightning. ¿ American Geophysical Union 1993