High-resolution optical spectroscopy of CPD -59°2636, one of the O-type stars in the open cluster Trumpler 16 in the Carina Nebula, reveals this object to be a multiple system displaying triple lines which we label as components A, B and C of spectral types O7 V, O8 V and O9 V, respectively. From our radial velocity measurements we find that the components A and B form a close binary with a period of 3.6284 d, and we obtain the first circular radial velocity orbit for this system with semi-amplitudes of 184 and 192 km s-1, leading to minimum masses of 10.1 and 9.7 M⊙. We find that the component C is a single lined binary with a period of 5.034 d and semi-amplitude of 48 km s-1. We also analyse the X-ray radiation from CPD -59°2636, finding neither appreciable overluminosity nor phase-related X-ray flux variations.Facultad de Ciencias Astronómicas y Geofísicas