Direct measurements of Ar^{+} 1s^{-1}2p^{-1}nl double-core-hole shake-up states are reported using conventional single-channel photoemission, offering a new and relatively easy means to study such species. The high-quality results yield accurate energies and lifetimes of the double-core-hole states. Their photoemission spectrum also can be likened to 1s absorption of an exotic argon ion with a 2p core vacancy, providing new information about the spectroscopy of both this unusual ionic state as well as the neutral atom.