The fluorescence lifetime of single DiI-dye molecules in a 20 nm polymer film on glass is measured as a function of the orientation of the absorption dipole moment. A strong dependence of the lifetime on the orientation of the dye molecules relative to the polymer/air interface is found. Molecules with a dipole moment perpendicular to the interface exhibit a lifetime which is by a factor of 2.1+/-0.1 longer than the lifetime of molecules with parallel dipole moments. The general trend of the results is in good agreement with theoretical predictions. However there are significant deviations which are attributed to varying molecular environments.