The electronic states of the ionic excimer Ar2++ are calculated using ab initio multireference configuration interaction and effective core pseudopotentials. Among states dissociating into Ar+(2P) + Ar+(2P), all are found to be repulsive, except the ground state, which occurs to be quasibound near R(e) = 4.1a0 with a well depth of greater-than-or-equal-to 230 cm-1. All states originating from Ar++(3P,1D,1S) + Ar are bound with dissociation energies in the range 3200-4500 cm-1 and equilibrium distances between 5.6a0 and 6a0. Simulation emission spectra from bound excited states are derived from the calculated potentials and the possible contribution of the Ar2++ ion to the third continuum fluorescence is discussed.