Highly correlated many-body perturbation theory (MBPT) and coupled-cluster (CC) calculations based on a single determinant reference function are applied to computation of the dissociation and atomization energies of ozone in its ground electronic state. While results obtained in SCF calculations are in error by > 100 kcal/mol for both quantities, many-body methods which include the effects of triply substituted determinants (MBPT (4) and CCSDT-1) yield values in relatively good agreement with experiment. The present results are found to be superior to those obtained in multireference configuration interaction studies (MRCI). Comparable accuracy is obtained with the empirically corrected G1 method and also in MRCI calculations, provided a correction is applied to account for the effects of unlinked clusters.