ArnCl- clusters have been investigated by anion zero electron kinetic energy (ZEKE) and partially discriminated threshold photodetachment spectroscopy. The experiments yield size-dependent electron affinities (EAs) and electronic state splittings for the X, I, and II states accessed by photodetachment. Cluster minimum energy structures have been determined from calculations based on a "simulated annealing" approach employing our recently presented Ar-Cl(-) pair potentials from anion ZEKE spectroscopy [T. Lenzer, I. Yourshaw, M. R. Furlanetto, G. Reiser, and D. M. Neumark, J. Chem. Phys. 110, 9578 (1999)] and various nonadditive terms. The EAs calculated without many-body effects overestimate the experimental EAs by up to 1500 cm(-1). Repulsive many-body induction in the anion clusters is found to be the dominant nonadditive effect. In addition, the attractive interaction between the chloride charge and the Ar-2 exchange quadrupole is important. These findings are consistent with our earlier results for XenI-, ArnI-, and ArnBr- clusters and highlight again the necessity of an adequate implementation of many-body effects to describe the energetics of such systems. For ArnCl-clusters with n > 12 we find some deviations between experimental and calculated (0 K) EA which can be explained by the population of less stable anion structures due to the finite temperatures of the clusters in our experiments. This results in lower EAs than predicted for the corresponding global minimum energy structures.