The cadmium thioindate spinel CdIn2S4 semiconductor has potential applications for optoelectronic devices. We present a theoretical study of the structural and optoelectronic properties of the host and of the Cr-doped ternary spinel. For the host spinel, we analyze the direct or indirect character of the energy bandgap, the change of the energy bandgap with the anion displacement parameter and with the site cation distribution, and the optical properties. The main effect of the Cr doping is the creation of an intermediate band within the energy bandgap. The character and the occupation of this band are analyzed for two substitutions: Cr by In and Cr by Cd. This band permits more channels for the photon absorption. The optical properties are obtained and analyzed. The absorption coefficients are decomposed into contributions from the different absorption channels and from the inter- and intra-atomic components.