The Large Eddy Simulation of non-premixed, turbulent, reacting flows is addressed. A new subgrid-scale chemistry model, previously proposed for incompressible, isothermal flows, is extended to the case of compressible combustion with multi-step, Arrhenius-rate reactions. The chemistry model predicts filtered chemical species concentrations and filtered reaction rates in a turbulent flow. It accounts for finite-rate chemistry by invoking the laminar flamelet approximation and employs an assumed form for the subgrid or "Large Eddy" Probability Density Function (LEPDF) of a mixture-fraction. It also uses an assumed counterflow form for the local scalar dissipation rate. Inputs to the chemistry model are the Favre-filtered mixture-fraction, its subgrid-scale variance, and filtered dissipation rate. The model is evaluated using (256)(3) point Direct Numerical Simulations of incompressible, nonisothermal decaying turbulence with a single-step reaction. Results indicate that, as the activation temperature is increased, the accuracy of the model degrades in an absolute sense but improves relative to an equilibrium chemistry assumption. Finally, it is also demonstrated that the assumed Beta distribution for the LEPDF yields reasonably accurate results for low (realistic) stoichiometric values of the mixture-fraction.