Absorption from seven intersystem (triplet-singlet) transitions of interstellar (CO)-C-12 were detected in ultraviolet spectra of zeta Oph. The observed equivalent widths are approximately consistent with the transitions' predicted f-values (Morton & Noreau 1994) and the (CO)-C-12 column density derived from the weakest of the observed A-X bands. These unsaturated intersystem transitions provide the opportunity to measure the (CO)-C-12 column density for heavily reddened (dense) sight lines. Laboratory measurements of oscillator strengths more precise than available ones will be needed to derive accurate column densities.