In this paper, the splitting of CO₂ in a pulsed plasma system, such as a dielectric barrier discharge (DBD), is evaluated from a chemical point of view by means of numerical modeling. For this purpose, a chemical reaction set of CO₂ in an atmospheric pressure plasma is developed, including the vibrational states of CO₂, O₂, and CO. The simulated pulses are matched to the conditions of a filament (or microdischarge) and repeated with intervals of 1 μs. The influence of vibrationally excited CO₂ as well as other neutral species, ions, and electrons on the CO₂ splitting is discussed. Our calculations predict that the electrons have the largest contribution to the CO₂ splitting at the conditions under study, by electron impact dissociation. The contribution of vibrationally excited CO₂ levels in the splitting of CO₂ is found be 6.4%, when only considering one microdischarge pulse and its afterglow, but it can be much higher for consecutive discharge pulses, as is typical for a filamentary DBD, when the interpulse time is short enough and accumulation effects in the vibrationally excited CO₂ densities can occur.