Cl atoms and SiO molecules are trapped in a solid Ar matrix at 16 K. The formation of the as yet unknown ClSiO molecule has been followed via its IR spectrum. The stretching frequencies of the isotopic isomer (ClSiO)-Cl-35-Si-28-O-16 are observed at 1160.9 and 509.4 cm(-1). Experiments with the O-18 isotopic isomers were performed in order to confirm the assignment of the absorptions and to characterize the force field. With the help of quantum chemical calculations (DFT) the optimized ClSiO bond angle is obtained at 125.2 degrees. The computed bond lengths are determined to be 153.6 pm for d(Si-O) and 207.8 pm for d(Si-O). The SiCl bond is weak in comparison with that of Cl2SiO (203.4 pm) which is in line with a decrease in the corresponding Si-Cl force constant. The calculation of its thermodynamic data, Delta(f)H(0)(298) = -167.2 kJ/mol; Delta(f)S(0)(298) = +279.1 J/(mol.K), is of high importance for high temperature gas phase reactions of industrial processes, e.g., the combustion of SiCl4 by O-2.