The fundamental electronic structure of the widely used battery material Li(x)CoO(2) still remains a mystery. Soft x-ray absorption spectroscopy of Li(x)CoO(2) reveals that holes with strong O 2p character play an essential role in the electronic conductivity of the Co(3+)/Co(4+) mixed valence CoO(2) layer. The oxygen holes are bound to the Co(4+) sites and the Li-ion vacancy, suggesting that the Li-ion flow can be stabilized by oxygen hole back flow. Such an oxygen hole state of Li(x)CoO(2) is unique among the various oxide-based battery materials and is one of the key ingredients to improving their electronic and Li-ion conductivities.