Lean premixed stratified combustion is rapidly growing in importance for modern engine designs. This paper presents large eddy simulations for a new burner design to assess the predictive capability of the probability density function (pdf) approach to flames that propagate through non-homogeneous mixtures in terms of equivalence ratio. Although various efforts have been made in the past for the simulation of the same test case the novelty of this work lies to the fact that it is the first simulation effort that differential diffusion is accounted for given the relatively low Reynolds numbers (13,800) of the configuration. First mean and root mean square velocity simulations are performed for the isothermal cases to assess the effect of the grid resolution and the overall LES flow field solver. Then instantaneous snapshots of the flame are presented to provide insight to the structure of the flame and the effect of stratification. Finally, results for velocities, temperature and mixture fraction are presented and compared with the experimental data. Overall, the results are in very good agreement with experiments.