Optically smooth Zn films supported on Cu-coated glass and quartz substrates have been obtained by physical vapor deposition of Zn in metallic form. The method employed involves resistive heating of a Mo boat tilled with high purity Zn shot in an Ar atmosphere at pressures of about 3-5 mTorr. Atomic force microscopy images revealed that the resulting Zn deposits consist of smooth features (rms roughness ca. 0.3 nm) with dimensions on the order of 200 nm. Preliminary results indicate that the electrochemical behavior of these films in strongly alkaline solutions is somewhat different than that observed for Zn in bulk commercial form.