The transition energies to the low-lying singlet and triplet excited states of Cr(CO)(6) are computed by equation-of-motion coupled cluster singles and doubles (EOM-CCSD) and similarity transformed equation-of-motion coupled cluster singles and doubles (STEOM-CCSD) methods with all-electrons basis sets. Both experimental and optimized geometries are used for the calculations. Calculations with various basis sets, among them one of the largest calculations performed at the EOM-CCSD level, based on atomic natural orbitals with 627 functions, were used to evaluate the basis set influence on computed transition energies. The presence of a shoulder at 3.9 eV in the experimental absorption spectrum, assigned to the (1)A(1g)-->(1)T(2u) transition, which was not reproduced by recent density functional theory (DFT) or multi-state complete active space perturbation theory (MS-CASPT2) is supported by the present STEOM-CCSD calculations with a theoretical value of 3.92 eV. In addition to this weak (1)A(1g)--> a (1)T(2u) absorption, we observe two strong absorptions corresponding to (1)A(1g)--> a (1)T(1u) at 4.37 eV (vs. an experimental value of 4.46 eV) and (1)A(1g)--> b (1)T(1u) at 5.20 eV (vs. an experimental value of 5.53 eV). Both are characterized as metal-to-ligand charge-transfer (MLCT) allowed transitions. The first metal-centered (MC) absorption at 4.37 eV in our best calculation is degenerate with the lowest MLCT absorbing state. The one-dimensional potential energy curves associated to the low-lying singlet MLCT and MC states as a function of the chromium axial carbonyl bond distance q(a) = [Cr-CO(axial)] show that an avoided crossing exists between the a (1)T(1g) (MC) and a (1)T(1u) (MLCT) states near 1.92 A, which is very close to the equilibrium Cr-CO distance. Moreover, the MC state seems to be dissociative for the CO loss. These two important features could explain the ultra-fast dissociation of CO (100 fs) observed in recent low intensity laser probed gas phase experiments.