A thermochemical analysis is performed in the system Cu-In-S at 723 K. Free energies of In6,S7, In417S583, “In2S3”, Cu951In49, and CuIn5S8 have been estimated, the numerical values (kJ/mol) of which are −1285, −97 780, −481.1, −31 680, and −1444. The free energy (kJ/mol) of CuInS2 is calculated from the relation G° = (-306.1 ± 54.4) + 0.5092T −1.397 10−5 T2 −0.09468T In T + 268.2T−1, which is obtained from published assessed standard formation enthalpy and specific heat and entropy data. The free energy of the Cu-In melt is taken from very new literature. A consistent set of data is used for the calculation of a tentative Gibbs triangle as well as of the corresponding predominance area diagram. The Gibbs triangle is calculated with the program thermo, the algorithm of which is given. The results are in agreement with the results of published measurements, also for the equilibria which involve the melt. The compound CuInS2, one of the possible base materials for thin film solar cells, is shown to equilibrate with most of the compounds of the system. Predictions are made how to prepare CuInS2 from Cu-In alloys and H2S/H2 gas mixtures. However, more experiments are necessary to establish the data, the experiments, and/or the results of the calculations.