Single and double excitation coupled-cluster [CCSD(T)] theory including an estimate of connected triple excitations by a perturbational treatment, calculations with a specially optimized [7s5p4d2 f] basis set, consisting of 168 contracted Gaussian-type functions, yield mean values <(beta)over bar> = -14.0 e(3)a(0)(3)E(h)(-2) and <(gamma)over bar>=2642 e(4)a(0)(4)E(h)(-3) for the first and second dipole hyperpolarizability of the open (C-2 upsilon) form of ozone. Due to the higher predictive capability of the CCSD(T) method and the improved completeness of the basis set, we expect these values to be more accurate than those obtained with the CCD+ST(CCD) method and a smaller [6s4p3d1 f] basis set [G. Maroulis, J. Chem. Phys. 101, 4949 (1994)]. The hyperpolarizability of the cyclic (D-3h) form of ozone, calculated with a [7s5p4d2 f] basis set optimized for the ring structure, is beta = -6.5 e(3)a(0)(3)E(h)(-2) and <(beta)over bar> = 1549 e(4)a(0)(4)E(h)(-3). In both symmetries, electron correlation changes drastically the self-consistent field picture of the hyperpolarizability tensor. Fourth-order Moller-Plesset perturbation theory is seen to predict very reliable values for the hyperpolarizability of the cyclic form. This is in marked contrast to the state of things brought forth by the study of the open form.