ALICE (A Large Ion Collider Experiment) is the experiment dedicated to the study of nucleus-nucleus collisions at the Large Hadron Collider (LHC). Its main physics goal is to characterize the properties of hot and dense nuclear matter created in heavy ion collisions, the so-called quark-gluon plasma (QGP). The forward part of ALICE consists of a muon spectrometer which is focused on the study of the production of heavy flavours and quarkonia via their (di)muon decay channels. This muon spectrometer is equipped of a trigger system based on four planes of large area Resistive Plate Chambers (RPCs) with 21,000 channels associated to a fast decision electronics. A commissioning phase was started in 2008 with the detection of cosmic rays and of the first beam injections into the LHC ring. In the presentation, design considerations and requirements will be discussed in view of lead-lead collisions. Next, the performances of the whole trigger system (detector and electronics) achieved in the commissioning will be presented, including the first tracks matched between the muon trigger and the muon tracking chambers.