We report on the growth of $CuCrO_2$ films using pulsed laser deposition and their structural and electrical transport properties. $CuCrO_2$ thin films were doped with 5 at% Mg for p-type properties. Epitaxial films of $CuCr_{0.95}Mg_{0.05}O_2$ were grown on c-plane sapphire substrates. The effects of growth temperature and oxygen pressure on film properties were investigated. The main phase of delafossite $CuCr_{0.95}Mg_{0.05}O_2$ was appeared above the growth temperature of $600^{circ}C$. The thin film grown at $500^{circ}C$ showed the highest conductivity, reaching 19.6 S/cm while higher growth temperatures over $500^{circ}C$ led to lower conductivity; the thin film grown at $700^{circ}C$ showed 0.02 S/cm.