We present a procedure to fabricate extremely smooth Au films supported on thin elastomeric (PDMS) Substrates. Minimum rms roughness and largest grain size are obtained using Si wafers, coated with native oxide and release layers, as templates for the growth of thermally evaporated Au films. The wafers are held at a temperature of 300 degrees C during deposition. The An films, up to 200 nm thick, are then transferred onto poly(dimethylsiloxane) substrates which have been previously surface-functionalized with a (3-mercaptopropyl)trimethoxysilane adhesion layer. The resulting Au films have been found by AFM to be extremely smooth with rms-roughness 2.5-4 angstrom and to exhibit a crystalline morphology with flat grains > 500 nm in size. Thinner films, down to 20 nm, are grown at lower temperature and are comparably smooth, but with a loss in crystalline morphology. We compare the results of this optimized procedure with other gold films grown on mica sheets as templates and to those produced using Ti-O-Si interfacial chemistry.