A polymer film having a thickness of 10 microns or less and improved barrier characteristics to both water vapor and oxygen is formed from a biaxially-oriented polypropylene film of isotactic polypropylene. The polypropylene is prepared by the polymerization of propylene in the presence of an isospecific metallocene catalyst. The film has a permeability to water vapor of less than about 2.5 g/m2 day/25 μm and a permeability to oxygen of less than about 2200 cc/m2 day/25 μm. The film also has a haze properties of less than about 1%. The polypropylene contains 0.1 to 1% 2,1 insertions and has an isotacticity of at least 96% meso pentads. The isotactic polypropylene thus produced is then extruded into a sheet that is biaxially-oriented by stressing the sheet in the transverse and longitudinal directions to a draw ratio of at least about 6:1 in the transverse direction, and at least about 4:1 in the longitudinal direction.