Zero electron kinetic energy (ZEKE) spectroscopy has been utilized to study the (ArCl-)-Ar-40-Cl-35 anion and the X1/2, I3/2 and II1/2 electronic states of neutral ArCl. Well-resolved progressions in the low-frequency vibrations of the anion and the neutral complexes are observed in the ZEKE spectra. From our spectroscopic data we construct model potential functions for the anion and three neutral states. This yields refined values for the neutral state splittings and the first accurate experimental ArCl- anion potential. Absolute uncertainties for R-m and epsilon in all potentials are estimated to be +/-0.08 Angstrom and +/-0.6 meV, respectively.