The three-dimensional intermolecular potential energy surface (IPS) for Ar-NH3 has been determined from a least-squares fit to 61 far infrared and microwave vibration-rotation-tunneling (VRT) measurements and to temperature-dependent second virial coefficients. The three intermolecular coordinates (R,theta phi) are treated without invoking any approximations regarding their separability, and the NH3 inversion-tunneling motion is included adiabatically. A surface with 13 variable parameters has been optimized to accurately reproduce the spectroscopic observables, using the collocation method to treat the coupled multidimensional dynamics within a scattering formalism. Anisotropy in the IPS is found to significantly mix the free rotor basis functions. The 149.6 cm(-1) global minimum on this surface occurs with the NH3 symmetry axis nearly perpendicular to the van der Waals bond axis (theta=96.6 degrees), at a center-of-mass separation of 3.57 Angstrom, and with the Ar atom midway between two of the NH3 hydrogen atoms (phi=60 degrees). The position of the global minimum is very different from the center-of-mass distance extracted from microwave spectroscopic studies. Long-range (R>3.8 Angstrom) attractive interactions are greatest when either a N-H bond or the NH3 lone pair is directed toward the argon. Comparisons with ab initio surfaces for this molecule as well as the experimentally determined IPS for Ar-H2O are presented.