A 59Co NMR study of CoO2, the x=0 end member of AxCoO2 (A=Na,Li,...) cobaltates, reveals a metallic ground state, though with clear signs of strong electron correlations: low-energy spin fluctuations develop at wave vectors q not equal to 0 and a crossover to a Fermi-liquid regime occurs below a characteristic temperature T* approximately 7 K. Despite some uncertainty over the exact cobalt oxidation state in this material, the results show that electronic correlations are revealed as x is reduced below 0.3. The data are consistent with NaxCoO2 being close to the Mott transition in the x-->0 limit.