The classic two-level or equivalent two-level model that only includes the statistical equilibrium of radiative and thermal processes of excitation and quenching between two vibrational energy levels is extended by adding chemical production to the rate equations. The modifications to the non-LTE source function and cooling rate are parameterized by phi_c that characterizes the ratio of chemical production to collisional quenching. For applications of broadband emission of O3 at 9.6-micron the non-LTE effect of chemical production on the cooling rate and limb emission is proportional to the ratio of O to O3 For a typical [O]/[O3] the maximum enhancements of cooling rate and limb radiance are about 0.03-0.05 K/day and 15-30%, respectively, both occurring near the mesopause regions. It is also shown that the broadband limb radiance above ~80 km is sensitive to O3 density but not to the direct cooling rate along the line-of-sight. This makes O3 retrieval feasible but the direct cooling rate retrieval difficult by using the O3 9.6-micron band limb emission.