Highly charged molecular ions are generated in Coulomb explosion experiments involving multielectron dissociative ionization, but little is known about the precise mechanisms involved in their formation. To help improve the understanding of such experiments, potential energy curves are calculated in this paper for diatomic chlorine (Cl₂) and its ions Cl₂ⁿ⁺, where n=1,2,3,4,6,8,10. Bound vibrational states are obtained in three low-lying electronic states for Cl₂²⁺ and one state for Cl₂³⁺. Vertical excitation energies are given for stepwise excitations up to Cl₂¹⁰⁺. For all the ions examined there is a significant energy defect (Δ) from the corresponding Coulomb potential, in one case reaching magnitudes of over 20 eV. We analyze the origin of these energy defects in terms of residual chemical bonding, and discuss the contribution of strongly bonding configurations at short internuclear distance. Finally, we present a simple physical model which describes the qualitative behavior of Δ(R,Q).