We present calculations of the thermal conductivity of fcc Argon at high pressures (pressure range is 10-150 GPa, temperatures range is 400-1200 K) from first principles in the framework of density functional theory and solution of the Boltzmann Transport Equation. Local density approximation (LDA) and generalized gradient approximation (GGA) produce similar thermal conductivities, with differences accounted by the known overbinding and underbinding of the LDA and GGA, correspondingly. Thermal conductivities at all considered pressures and temperatures are found to be consistent with the results of previous molecular dynamics simulations based on classical 2-body potentials. However, they are not consistent with recent experimental findings. Possible reasons for this disagreement are discussed. In addition, in light of our calculations, we critically examine analytically tractable approximations for thermal conductivity as applied to solid argon. V C 2013 AIP Publishing LLC. [http://dx.