A diffraction experiment is described in which 1.065 Å neutrons are incident on gaseous 36Ar at a density of 2.52 × 1021 atoms/cm3 and temperature of 141.3 K. Information accurate to 1% is obtained on the structure factor S(Q) in the wave-number range 0.5 Å-1 < Q < 6.3 Å-1. Using both HNC and the Percus-Yevick theory the pair potential ϕ(r) for Ar is derived from a set of S(Q) data. This set of data is extended to Q = 0 and Q = 13 Å-1 in such a way that, within the core of the potential, the pair correlation function is zero and the correct hydrodynamic limit for S(Q) is obtained. The locations of ϕ(r) = 0 and dϕ(r)/dr = 0 are found to be (3.28 ± 0.01) Å and (3.81 ± 0.01) Å, respectively, whereas the depth ε/k = (124 ± 4) K. The pair potential, which is tabulated, is compared with the one discussed by Dymond and Alder and some analytic potentials. In the appendices a new correction to the static approximation and a relation for the damping of oscillations in S(Q) at large Q values are calculated.