Three-dimensional direct numerical simulation of a spatially developing slot-burner Bunsen flame has been performed. The simulation is aimed at better understanding the dynamics of turbulent premixed flames in the thin reaction zones regime. A reduced chemical model for methane-air chemistry consisting of 13 resolved species, 4 quasi-steady state species and 73 elementary reactions has been developed specifically for the current simulation. Using the new chemical model a lean premixed methane-air flame at preheated conditions and ambient pressure is simulated. The simulation is performed long enough to achieve statistical stationarity. The data is analyzed to study possible influences of turbulence on the flame thickness. The results show that the average flame thickness increases, in agreement with a few, although not unanimous, experimental results.