Often in combustion engineering, when unpremixed gaseous reactants are burned in a low-speed shear flow, product formation is controlled by the rate of mixing, rather than by the rate of reaction. The reaction mechanism is usually modeled as a direct one-step irreversible reaction, with Lewis-Semenov number taken as unity. For laminar flow, Burke and Schumann suggested how knowledge of a passive scalar in the same flow field as the reactants, satisfying similar boundary conditions, and possessing identical diffusion coefficients, furnishes the diffusion-flame solution. Analogously, for the turbulent case, under almost identical constraints, Toor indicated how knowledge of the mean field and probability density function for a passive scalar in an inert flow yields the mean-field behavior of the turbulent diffusion flame in the same flow. The only additional condition is that, in general, the heat associated with chemical reaction must not alter the dynamics. Here, Toor's method is extended to the two-step symmetrical chain reaction of interest in chemical lasers. The highly nonGaussian probability density function implied by large-scale turbulent structure observed in, at least, portions of the two-dimensional mixing layer downstream of a splitter plate is developed further.