Since its discovery, the superconducting phase in water-intercalated sodium cobaltates Na(x)CoO2·yH2O (x∼0.3, y∼1.3) has posed fundamental challenges in terms of experimental investigation and theoretical understanding. By a combined cluster calculation and renormalization group approach, we find an anisotropic chiral d+id-wave state as a consequence of multiorbital effects, Fermi surface topology, and magnetic fluctuations. It naturally explains the singlet property and close-to-nodal gap features of the superconducting phase as indicated by experiments.