We investigate the structural, electronic, and optical properties of the mixed chalcogenide-halide bismuth perovskites CH3NH3BiChI2 (Ch = S, Se, Te) using the relativistic all-electron calculations. We use the structural model where the Ch atoms are placed at the apical position in the BiCh2I4 octahedron. It is found that the structures of CH3NH3BiChI2 are contracted in the apical direction and the Bi–Ch bond lengths decrease in the order of Ch = S, Se, and Te. CH3NH3BiChI2 exhibit anisotropic optical properties and show higher absorption coefficients than CH3NH3PbI3. Furthermore, employing the spectroscopically limited maximum efficiency as a metric for quantifying the photovoltaic performance, we find that CH3NH3BiSI2 and CH3NH3BiSeI2 are promising candidates for thin-film solar cells.