We report the structural, electronics and optical properties of oxychalcogenide compounds CuRhOX (X= S, Se, Te) using state-of-the-art density functional theory (DFT). The structural geometry of these oxychalcogenides is same as the delafossite compounds. The electronic band structures reveal the semiconducting nature with an indirect band gap of 1.06, 0.90 and 0.69 eV for CuRhOS, CuRhOSe and CuRhOTe respectively. The partial density of states (PDOS) depicts the major contribution of O-2p and X-2p states near the valence band maximum (VBM). The dielectric constants and optical absorption spectra show the strong optical absorption in visible region indicating their potential applications in optoelectronics. [ABSTRACT FROM AUTHOR]