The structure of supercritical argon at 350 K over a broad range of density (pressures between 5 to 90 MPa) is determined experimentally by high-pressure neutron diffraction, and theoretically from quantum chemically calculated ab initio pair potentials applied in molecular dynamics simulations. The origins of small discrepancies between theory and experiment are discussed. Together with previous results at 85 K in the liquid state, the overall agreement between theory and experiment, over a wide range of state points, is found to be quite good. This is remarkable, as no empirical parameters are used for the calculations.