Prompt gamma rays of cerium and chlorine were investigated with the FaNGaS (Fast Neutron-induced Gamma-ray Spectrometry) instrument operated at the Heinz Maier-Leibnitz Zentrum (MLZ) in Garching. The gamma radiation was emitted from (n,n’), (n,p) and (n,α) reactions induced by the irradiation of a cerium(III) chloride (CeCl3) sample with a beam of fission neutrons. Additionally, a polyvinylchloride (PVC, (C2H3Cl)n) sample was irradiated to verify possible interferences between gamma lines of cerium and chlorine. We identified 87 prompt gamma lines of cerium and chlorine. From these, we assigned 58 lines to the (n,n’) reaction in cerium (one for 136Ce, 41 for 140Ce and 16 for 142Ce), 23 to the (n,n’) reaction in chlorine (15 for 35Cl and 8 for 37Cl), 5 lines to the 35Cl(n,p)35S reaction and 1 line to the 35Cl(n,α)32P reaction. We present relative intensities and fast-neutron spectrum-averaged partial cross sections of the aforementioned gamma lines and compare them with available literature data. Identification of new lines and discussion of possible errors adds important value to the literature data found to be consistent with our results. In addition, for a counting time of 12 h we estimate the detection limits for cerium and chlorine as 1 and 2 mg, respectively.