Based on the Libby Williams analysis of partially premixed turbulent combustion, a new closure model is proposed that allows the calculation of a two-scalar probability density function (PDF) that is used to evaluate mean chemical rates. This model requires the use of transport equations for only mean and intensities of the two independent thermodynamic quantities, namely, the fuel mass fraction and a mixture fraction. Application is made to the calculation of a turbulent flame stabilized in a shear layer obtained by mixing a stream of premixed reactants with a stream of hot combustion products; these two streams initially have different equivalence ratios. A complete analysis of this situation, including the evolution of the PDF, is presented. Moreover, calculated mean temperature and fuel mass fraction profiles are compared successfully with available experimental data.