High-fidelity Large Eddy Simulations (LES) are performed to study the effect of hydrogen injection on a lean turbulent CH4 /Air premixed flame. An Analytically Reduced Chemistry (ARC) mechanism is used to achieve a detailed description of CH4/Air-H2 chemistry. First, a validation of this kinetic scheme against the detailed GRI-Mech 3.0 mechanism is presented considering both simplified and complex transport properties. When hydrogen is added to the mixture, large variations of the mixture Prandtl and of the N2 Schmidt numbers are observed depending on the local species concentrations, features that are missed by simplified models. LES is then applied to study the structure and stabilization mechanisms of a lean (φ = 0.8) premixed CH4/Air swirled flame enriched with hydrogen by using different transport modeling strategies. First, the fully pre- mixed CH4/Air case is considered and results are found to validate the LES approach. In agreement with experiments, a classical V-shape flame is stabilized in the low-velocity region near the flame holder created by a central recirculation zone (CRZ). Then, hydrogen enrichment is achieved injecting 2% of the CH4 thermal power with a central fuel injection lance. Both premixed and diffusion flame branches are present in this case, impacting flame stabilization and flame angle. The flame root of the main premixed flame is stabilized by a diffusion flame kernel created by the injected hydrogen reacting with the oxygen in excess of the premixed stream. Moreover, the H2 consumed with the remaining oxygen in burnt gases leads to the formation of a second flame branch inside the CRZ which is responsible of an increase of the flame angle. Given the high concentration of hydrogen, an impact of the molecular transport models is observed on the flame lift-off height highlighting the importance of using complex transport properties in any LES involving hydrogen combustion.