Ab initio calculation of electronic excitation energies with chemical accuracy (ca. 1 kcal·mol-1 or 0.043 eV with respect to experiment) is a long-standing challenge in electronic structure theory. Indeed, the most advanced theories can, in practice, only be used to estimate vertical transition energies that cannot be measured experimentally, whereas the calculation of 0-0 energies requires excited-state structures and vibrations for both the ground and excited states, which drastically restrains the number of applicable methods. In this Letter, we present a composite computational protocol able to deliver chemically accurate theoretical 0-0 energies, with a mean absolute deviation of 0.018 eV for a set of 35 singlet valence states. Such accuracy, achievable for the valence states of small- and medium-sized molecules only, allows pinpointing questionable experimental assignments with very high confidence and constitutes a step toward quantitative prediction of excited-state properties.