Single phase, epitaxial, transparent, and p-type CuAlO2 films are successfully grown on c-plane sapphire by polymer-assisted deposition. At wavelengths in the range of 400-1000 nm, the optical transmittance of the films is 60-80%. The energy band gap is 3.6 eV. The as-synthesized CuAlO2 films are highly resistive, with room-temperature resistivity around 10(5) Omega cm. The resistivity can be reduced to 10(3)-10(4) Omega cm by post-annealing films in oxygen.