Since its discovery, the superconducting phase in water-intercalated sodium cobaltates NaxCoO2 center dot yH(2)O (x similar to 0.3, y similar to 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.