Electron paramagnetic resonance experiments have shown that, depending on the doping procedure, two different S2− centers may coexist in KCl. These centers have the 2B2g and the 2B3gground state, respectively. As no experimental ligand hyperfine data are available, it could not be determined whether the S2− molecular ion replaces a single halide ion (mono-vacancy site) or two nearest neighbor halide ions (di-vacancy site). Also, other defect models could a priory be considered. In this work, cluster in vacuo density functional theory calculations of the g and 33S hyperfine tensors show that the S2− ion at a mono-vacancy site has the 2B2g ground state, whereas S2− in a di-vacancy exhibits a 2B3g ground state. For the latter center, the possibility of charge compensation by a cation vacancy is also considered. The calculations indicate that a possible vacancy is not in the direct vicinity (nearest or next-nearest neighbor) of the S2− ion.