Diffraction of neutrons from 36 Ar monolayers adsorbed on graphite basal planes indicates that an ordered, two-dimensional (2D) triangular lattice is formed at low temperature. The lattice constant is found to be slightly larger than that of the bulk 3D solid but significantly smaller than that of a registered √3×√3 overlayer. Thermal expansion of the monolayer is anomalously large; up to 60 K the linear expansion is 4.5 times greater than in the 3D solid. There is no evidence of a sharp melting transition. Instead, the positional correlations (which extend to the full dimensions of the crystallite surfaces at low temperatures) are observed to decrease smoothly above 40 K, falling from 100 to 15 Å at 80 K. Little if any positional order remains at temperatures where the nearest-neighbor distance in the monolayer matches that of a registered √3×√3 phase. The spectrum of neutrons inelastically scattered from 36 Ar monolayers in the nominally in-plane configuration can be reasonably well described at low temperatures by a 2D harmonic-phonon model while the scattering in the out-of-plane configuration seems to be best represented in terms of a resonant coupling of the monolayer film to out-of-plane collective motions of the graphite substrate. There is some evidence of renormalization of the in-plane transverse modes of the monolayer at higher temperatures; however, the in-plane longitudinal modes and the out-of-plane modes do not appear to be similarly affected.