Indium monochloride, InCl, adds HCl or H-2 when isolated together with these molecules in an argon matrix at 12 K and photoactivated by broad-band UV-visible radiation. On the basis of the infrared spectra of the matrices (including the effects of H-1/H-2 and Cl-35/Cl-37 isotopic change) and of density functional theory (DFT) calculations, the products of the reactions were identified as the discrete indium hydride molecules HInCl2 and H2InCl. HInCl2 is also one of the products of the reactions brought about by photolysis of matrices containing In atoms and HCl; both HGaCl2 and H2GaCl are formed from Ga atoms under similar conditions. All six vibrational fundamentals (3a(1) + 1b(1) + 2b(2)) of (HInCl)-In-2 and five of the six vibrational fundamentals of HInCl2 have been identified; normal coordinate and DFT calculations provide a framework for evaluating the physical properties of the two molecules.