A thermoplastic container or packaging material is given low oxygen permeability by coating with a crosslinked acrylate layer and a layer of oxygen barrier material deposited over the acrylate layer. Another acrylate layer may be deposited over the oxygen barrier. The oxygen barrier is selected from the group consisting of silicon oxide, aluminum oxide and metal. The acrylate layer may be formed from a photopolymerizable polyfunctional acrylate that is sufficiently low viscosity to be sprayed on the substrate or applied by dipping. Alternatively, the acrylate layer is a polymerization product of an acrylate monomer which is evaporated in a vacuum, condensed on the substrate and polymerized by irradiation by ultraviolet or an electron beam. The surface of the thermoplastic substrate is prepared for deposition of the acrylate by either flame treating the surface of the substrate to heat it above its melting point without deforming the substrate to thereby smooth the surface, or by plasma treating the surface for enhancing adhesion of the acrylate. Chilling the substrate enhances deposition efficiency.