Using first principles calculations we describe the energy band structure of bulk CuInS2. The energy band parameters for the multiband effective mass approximation that describes the band edges of this semiconductor are obtained by fitting them to the first principles spectra. Within the multiband effective mass approximation we develop a theoretical description for the structure of band-edge levels and optical properties of the CuInS2 nanocrystals. For the nanocrystals of spherical shape, the optical transitions are weakly allowed between the electron and hole ground states due to the tetragonal symmetry of the crystal lattice, resulting in a large Stokes shift of photoluminescence up to 300 meV in the smallest nanocrystals. This theory of the band-edge optical transitions in CuInS2 NCs can be applied to spherical NCs made of other chalcopyrite compounds.