We determined the zero-density viscosity eta(Ar)(0,T) and thermal conductivity lambda(Ar)(0,T) of argon with a standard uncertainty of 0.084% in the temperature range 200 K to 400 K. This uncertainty is dominated by the uncertainty of helium's viscosity eta(He)(0,T), which we estimate to be 0.080% based upon the difference between ab initio and experimental values at 298.15 K. Our results may improve (1) the argon-argon interatomic potential, (2) calculated boundary-layer corrections for primary acoustic thermometry, and (3) calibrations of laminar flow meters as well as instruments for measuring transport properties. At 298.15 K, we determined the ratio eta(Ar)(0,298)/eta(He)(0,298) = 1.138 00 +/- 0.000 13 from measurements of the flow rate of these gases through a quartz capillary while simultaneously measuring the pressures at the ends of the capillary. Between 200 K and 400 K, we used a two-capillary viscometer to determine eta(Ar)(0,T)/eta(He)(0,T) = 1.211 67 - 0.820 34 exp(-T/123.78 K) with an uncertainty of 0.024%. From eta(Ar)(0,T)/eta(He)(0,T), we computed eta(Ar)(0,T) using the values of eta(He)(0,T) calculated ab initio. Finally, we computed the thermal conductivity of argon from eta(Ar)(0,T) and values of the Prandtl number that we computed from argon - argon interatomic potentials.