  The in-plane resistivity, rho, and thermal conductivity, kappa, of a single
crystal of Na_0.7CoO_2 were measured down to 40 mK. Verification of the
Wiedemann-Franz law, kappa/T = L_0/rho as T -> 0, and observation of a T^2
dependence of rho at low temperature, rho = rho_0 + AT^2, establish the
existence of a well-defined Fermi-liquid state. The measured value of
coefficient A reveals enormous electron-electron scattering, characterized by
the largest Kadowaki-Woods ratio, A/gamma^2, encountered in any material. The
rapid suppression of A with magnetic field suggests a possible proximity to a
magnetic quantum critical point. We also speculate on the possible role of
magnetic frustration and proximity to a Mott insulator.
