Direct numerical simulation of a three-dimensional spatially-developing turbulent Bunsen flame has been performed at three different turbulence intensities. The simulations are performed using a reduced methane-air chemical mechanism which is specifically tailored for the lean premixed conditions simulated here. A planar-jet turbulent Bunsen flame configuration is used in which turbulent preheated methane-air mixture at 0.7 equivalence ratio issues through a central jet and is surrounded by a hot laminar coflow of burned products. The turbulence characteristics at the jet inflow are selected such that combustion occurs in the thin reaction zones (TRZ) regime. At the lowest turbulence intensity the conditions fall on the boundary between the TRZ regime and the corrugated flamelet regime. At the highest turbulence intensity the conditions correspond to the boundary between the TRZ regime and the broken reaction zones regime. The data from the three simulations is analyzed to understand the effect of turbulent stirring on the flame structure and thickness. Statistical analysis of the data shows that the thermal preheat layer of the flame is thickened due to the action of turbulence, but the reaction zone is not significantly affected.