We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl−) in the range of 10 meV–100 eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl− using ab initio binding energies and positronic wave functions at both the mean-field and correlated levels extrapolated to the complete basis set limit. The accuracy of these ab initio data was benchmarked on the PsF system with the existing highly accurate results, including the very recent quantum Monte Carlo results. We have investigated Ps excited states up to n = 4. The results suggest that the channel Ps(n = 2) is of particular interest for the production of PsCl in the ground state and shows that an accurate treatment of correlation effects (i.e., electron–electron and electron–positron correlations) leads to a significant change in the magnitude of the PsCl production cross section with respect to the mean-field level.