H.E.S.S.-The High Energy Stereoscopic System-is a new system of large atmospheric Cherenkov telescopes for GeV/TeV γ-ray astronomy. This paper describes the trigger system of H.E.S.S. with emphasis on the multi-telescope array level trigger. The system trigger requires the simultaneous detection of air-showers by several telescopes at the hardware level. This requirement allows a suppression of background events which in turn leads to a lower system energy threshold for the detection of γ-rays. The implementation of the H.E.S.S. trigger system is presented along with data taken to characterise its performance.