Thin films of a delafossite compound CuScO2 were grown on spinel MgAl2O4 (111) substrates, yielding in highly crystalline and (0001)-oriented epitaxial structures. Absorption spectra at 20 K revealed a sharp exciton resonance at 3.97 eV, which persisted up to 300 K. Its direct transition band gap at 20 K and exciton binding energies were determined to be about 4.35 and 380 meV, both of which are considerably larger than those of ZnO. In view of its capability of naturally layered structure and p-type doping, this compound will be interesting for exciton physics as well as implementation of heterostructured devices.