When an electron binds to its anti-matter counterpart, the positron, it forms the exotic atom positronium (Ps). Ps can further bind to another electron to form the positronium negative ion, Ps(-) (e(-)e(+)e(-)). Since its constituents are solely point-like particles with the same mass, this system provides an excellent testing ground for the three-body problem in quantum mechanics. While theoretical works on its energy level and dynamics have been performed extensively, experimental investigations of its characteristics have been hampered by the weak ion yield and short annihilation lifetime. Here we report on the laser spectroscopy study of Ps(-), using a source of efficiently produced ions, generated from the bombardment of slow positrons onto a Na-coated W surface. A strong shape resonance of (1)P(o) symmetry has been observed near the Ps (n=2) formation threshold. The resonance energy and width measured are in good agreement with the result of three-body calculations.