The adsorption of xenon on the sodium chloride (001) surface has been studied using high-resolution helium atom scattering. From the temperature dependence of the specular intensity in the range between 27 and 70 K under isobaric conditions the heat of adsorption of the Xe monolayer was determined to be E-ads=19.2+/-2 kJ/mol. At monolayer coverage, helium atom diffraction measurements reveal that a strained quasi-hexagonal superstructure is formed, which differs from the well-known hexagonal structure of the Xe bulk, and has a c(10 x 2) symmetry. The perpendicular frustrated translation vibrational energy was measured with helium atom time-of-flight spectroscopy to be 2.5 meV and showed an avoided crossing with the NaCl surface Rayleigh mode. A further dispersive mode of the monolayer has been assigned to a longitudinal in-plane mode of the Xe layer. As found for Xe monolayers on several low index copper surfaces the best fit radial force constant for this mode is a factor of four smaller than deduced from the Xe-Xe gas-phase potential.