We present very accurate orbital parameters and mass measurements (2.4% accuracy) for the well known very low mass triple system Gl 866. We obtain first orbital elements for the short-period orbit and greatly improve the long period orbit. All three stars have masses close to 0.1 M_sun, and the system thus provides the strongest constraints to date on the mass-luminosity relation close to the brown dwarf limit. Based on observations made at the Observatoire de Haute Provence (CNRS), and at the CFH Telescope, operated by the NRCC, the CNRS and the University of Hawaii. Table 3 is only avaliable electronically with the On-Line publication at http://link.springer.de/link/service/journals/00230/