Results are presented from a theoretical study of the lower electronic states of the CUO molecule. Multiconfigurational wave functions have been used with dynamic correlation added using second order perturbation theory. Extended basis sets have been used, which for uranium were contracted including scalar relativistic effects. Spin orbit interaction has been included using the state-interaction approach. The results predict that the ground state of linear CUO is phi2 with the closed shell sigma(+)0 state 0.5 eV higher in energy. This is in agreement with matrix isolation spectroscopy, which predicts phi2 as the ground state when the matrix contains noble gas atoms heavier than Ne. In an Ne matrix, the experiments indicate, however, that CUO is in the sigma(+)0 state. The change of ground state due to the change of the matrix surrounding CUO cannot be explained by the results obtained in this work and remains a mystery.