While the accuracy of chemical kinetic mechanisms continues to improve, these mechanisms are still models with, sometimes considerable, uncertainty. In order to rigorously validate turbulent combustion simulations against experimental data, this uncertainty must be separated from deficiencies in the turbulent combustion model itself. In this work, a method is developed for quantifying the uncertainty in turbulent flame simulations due to input uncertainty in the chemical mechanism. Here the method is developed for Large Eddy Simulation (LES) combined with a steady flamelet model. Rather than a brute force approach in which hundreds or thousands of LES runs are required, the method takes advantage of the actual algorithm employed with the steady flamelet model. First, the uncertainty in the chemical kinetics is propagated through the flamelet equations, and the resulting joint distribution is used as a stochastic equation of state in the LES. Direct uncertainty in temperature and species mass fraction is obtained by sampling over the joint distribution as statistics are collected. Uncertainty due to "active" quantities such as density, viscosity, diffusivity, etc., is propagated using non-intrusive stochastic collocation, requiring a few LES runs.