Using homogeneous lean mixtures is an efficient way to reduce fuel consumption and pollutant emissions in internal combustion engines. However, lean combustion requires breakthrough technologies to induce reliable ignition and fast combustion. One of these technologies uses pre-chamber to create multiple hot turbulent jets and provide ignition sites for the lean mixture. In this paper, the behaviour of a pre-chamber ignition system used to ignite the main chamber of a real engine is studied using large eddy simulation with direct integration of analytically reduced chemistry using the dynamic thickened flame model. The large eddy simulation allows to analyze the flow entering and leaving the pre-chamber, to measure the cooling and quenching effects introduced by the hot gas passages through the ducts connecting pre-and main chambers and to analyze the ignition and combustion sequences. For the case studied here, small amount of flame kernels are exhausted from the pre-chamber. Hot products penetrate the main chamber, disperse and mix with the fresh reactants and lead to ignition. The combustion in the main chamber starts in a distributed reaction mode before reaching a flamelet propagation mode.