The in-plane resistivity ρ and thermal conductivity к of a single crystal of NaxCoO2 (x = 0.7) were measured down to 40 mK. Verification of the Wiedemann-Franz law, к/T = L0/ρ as T→0, and observation of a T2 dependence of ρ at low temperature, △ρ= AT2, establish the existence of a well-defined Fermi-liquid state. The measured value of coefficient A reveals enormous electronelectron scattering, characterized by the largest Kadowaki-Woods ratio A/γ 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.