Low temperature photoluminescence (PL) measurement of a deep-donor-deep-acceptor (DD-DA) pair recombination emission of close DA pairs in CuInS2 at v = 0.62 eV reveals two well resolved lattice vibrational modes, of energy (h) over bar omega (1) = 40.5 meV and (h) over bar omega (2), = 8 meV. Furthermore, the recombination emission has an additional fine structure of Delta E= 2 meV. It appears that the 2 meV fine structure can be interpreted as being due to a small difference in the DA separation between two otherwise equivalent interstitial donor sites. This is due to the tetragonal lattice distortion in the CuInS2 structure. The measured full width at half maximum, inclusive of instrumental resolution, of these two zero-phonon-emission lines was approximately 0.6 meV at T=8 K.