The unprecedented design intensities of the LHC require several important advances in beam collimation. With its more than 100 collimators, acting on various planes and beams, the LHC collimation system is the biggest and most performing such system ever designed and constructed. The solution for LHC collimation is explained, the technical components are introduced and the initial performance is presented. Residual beam leakage from the system is analysed. Measurements and simulations are presented which show that collimation efficiencies of better than 99.97 % have been measured with the 3.5 TeV proton beams of the LHC, in excellent agreement with expectations.