A gas turbine model combustor is studied using Large Eddy Simulation with a transported Probability Density Function approach solved by the Eulerian stochastic field method. The chemistry is represented by a reduced methane mechanism containing 15 steps and 19 species while the subgrid scale stresses and scalar fluxes are modelled, respectively, via a dynamic Smagorinsky model and a gradient diffusion approximation. The test case comprises a partially premixed swirl flame in a complex geometry. Four stochastic fields are utilised in the simulations, which are performed for two different combustor operating conditions involving a stable and an unstable flame. Good agreement between the simulation and measurement data is shown in a comparison of mean velocity, temperature and species mass fraction profiles, as well as scatter plots of the instantaneous thermochemical properties. In conclusion, the predictive capabilities of the employed Large Eddy Simulation method are successfully demonstrated in this work.