Spin-resolved O 1s x-ray absorption measurements on CrO2 reveal that the spin polarization of the states at the Fermi level approaches 100%, providing direct evidence of the half-metallic nature of CrO2. The measurements also show the existence of an atomiclike Cr 3d state not far away from the Fermi level with a spin polarization of only 50%, establishing its Mott-Hubbard character. We conclude that CrO2 has a dualistic electronic nature, in which the states at the Fermi level are bandlike, while those at higher energies are strongly localized of completely different origin and symmetry. The finding of an exceptionally large number of O 2p holes suggests their important role in preventing the strongly correlated CrO2 from being an insulator.