A global potential energy surface ͑PES͒ for the 1 4 AЈ spin-aligned state of Li 3 is presented. The surface is constructed as a many body expansion of the potential which is the sum of pairwise additive two-body potentials plus a three-body term. The two-body potential is that for the a 3 ⌺ u ϩ state of the lithium dimer. It combines the most recent Rydberg-Klein-Rees potential available ͓A. Ross ͑private communication͔͒ with well-known short and long range expansions and accurately reproduces all known experimental data. To obtain the three-body contributions, an ab initio PES was computed at 1122 points using full configuration interaction for the three valence electrons with an augmented Gaussian basis and the effective core potentials of Stevens, Basch, and Krauss ͓W. J. Stevens et al., J. Chem. Phys. 81, 6026 ͑1984͔͒ for the other electrons. The two-body interactions are also calculated using the same basis and then subtracted from the full interaction to give the three-body term. To construct the three-body potential at arbitrary configurations we use interpolation for small perimeters of the triangle formed by the triatomic system and an analytic fitting function for large perimeters. A switching function guarantees the smoothness of the potential function everywhere. The equilibrium position occurs at D 3h symmetry with a bond distance of 5.861a 0 , nearly 2a 0 smaller than the equilibrium value of 7.886a 0 of the lithium dimer. The well depth at the equilibrium is 4112.64 cm Ϫ1 . This is considerably deeper than the well depth of 1001.22 cm Ϫ1 for the pairwise additive potential at its equilibrium. Three-body effects are even more important for Li 3 than in the recently reported Na 3 case ͓J. Higgins et al., J. Chem. Phys. 112, 5751 ͑2000͔͒, and the nonadditive three-body term cannot be neglected in any calculation on this system.