Large-Eddy Simulation (LES), coupled with the Conditional Moment Closure (CMC) sub-grid model and the GRI3 detailed chemical mechanism, are used to explore the structure of the Delft III piloted turbulent non-premixed flame. The use of a quite refined multi-dimensional CMC grid and the detailed chemistry, together with the capability of LES to follow local fluctuations of the scalar dissipation, allow the prediction of localised extinctions and re-ignitions in locations consistent with experiment. The statistics of velocity, mixture fraction, temperature, mass fractions of the major species and of OH are overall in good agreement with experimental data. Carbon monoxide is captured very well, but NO is overpredicted, perhaps due to inherent limitations of the GRI3 scheme to capture NO emissions.