The photocatalytic conversion of carbon dioxide to liquid fuels with electrons taken from water with solar photons is one of the grand goals of renewable energy research. Polymeric carbon nitrides recently emerged as metal-free materials with promising functionalities for hydrogen evolution from water as well as the activation of carbon dioxide. Molecular heptazine (Hz), the building block of polymeric carbon nitrides, is one the strongest known organic photo-oxidants and has been shown to be able to photo-oxidize water with near-visible light, resulting in reduced (hydrogenated) heptazine (HzH) and OH radicals. In the present work, we explored with ab initio computational methods whether the HzH chromophore is able to reduce carbon dioxide to the hydroxy-formyl (HOCO) radical in hydrogen-bonded HzH-CO2 complexes by the absorption of a photon. In remarkable contrast to the high barrier for carbon dioxide activation in the electronic ground state, the excited-state proton-coupled electron transfer (PCET) reaction is nearly barrierless, but requires the diabatic passage of three conical intersections. The possibility of barrierless carbon dioxide activation by excited-state PCET has so far not been taken into consideration in the interpretation of photocatalytic carbon dioxide reduction on carbon nitride materials.