We report the first global ab initio-based potential energy surface (PES) for ground-state triplet C-3((3)A') based on accurate energies extrapolated to the complete basis set (CBS) limit, and using the combined hyperbolic-inverse-power-representation method for the analytical modeling. By relying on a cost-effective CBS(D,T) protocol, we ensure that the final form reproduces all topographical features of the PES, including its cyclic-linear isomerization barrier, with CBS(5,6)-quality. To partially account for the incompleteness of the N-electron basis and other minor effects, the available accurate experimental data on the relevant diatomics were used to obtain direct-fit curves that replace the theoretical ones in the many-body expansion. Besides describing properly long-range interactions at all asymptotic channels and permutational symmetry by built-in construction, the PES reported here reproduces the proper exothermicities at dissociation regions as well as the spectroscopy of the diatomic fragments. Bound vibrational state calculations in both linear and cyclic isomers have also been carried out, unveiling a good match of the available data on C-3((a) over tilde (3)Pi a, while assisting with IR band positions for C-3((3)A'(2)) that may serve as a guide for its laboratory and astronomical detection.