The symmetry adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) theories are applied to the calculations of the ground and excited states of the chromate ion CrO42-. Electron correlations are very large for this molecule and work to relax the charge polarization of the Cr-O bonds in the ground state. The experimental spectrum of CrO42- is well reproduced by the present calculations, which is the first ab initio study of the excited states including electron correlations. All of the observed peaks are assigned to the dipole allowed transitions to the T-1(2) excited states. Furthermore, many kinds of forbidden transitions are calculated in the lower energy region. Both allowed and forbidden transitions are characterized as the electron-transfer excitations from oxygen to metal. In comparison with the previous theoretical studies, the present SAC-CI results are in good agreement with experiment and give reliable assignments of the spectrum. We also compare the electronic structures and spectra of CrO42-, MoO42-, MnO4-, RuO4, and OSO4, which have been studied by the SAC and SAC-CI methods.