We report on a global potential energy hypersurface for the upper sheet of the lowest triplet state of H-3(+). The analytic representation is based on the double many-body expansion theory. The ab initio data points, calculated with a large cc-pV5Z basis, are represented with a root mean square deviation of only 5.54 cm(-1) in the energy region below the H++2H(S-2) dissociation threshold. The quasi-bound vibronic states supported by this surface have also been calculated. (C) 2004 American Institute of Physics.