Context. Sulphur is chemically versatile and ubiquitous, and important in both planetary and astrochemical processes. Compared to its cosmic abundance, it appears to be significantly depleted in dense interstellar regions - a phenomenon that is the subject of ongoing research. Comets, which retain material from the early Solar System, provide a valuable record for assessing sulphur reservoirs and their isotopic compositions. Comet 67P/Churyumov-Gerasimenko was particularly suitable for in situ investigation. Aims. This study aims to determine the 34S/32S isotopic ratios of CS2 in comet 67P/Churyumov-Gerasimenko and to investigate if the CS2 isotopologue double ratio, 12C34S2/12C34S32S-to-12C34S32S/12C32S2, is consistent with the statistically expected value. Methods. We analysed high-resolution spectra acquired by the ROSINA Double Focusing Mass Spectrometer (ROSINA/DFMS) in March 2016, when the Rosetta spacecraft was within 17 km of the nucleus and the CS2 signal was high. Three CS2 isotopologues, 12C32S2, 12C34S32S, and 12C34S2, were used to derive three 34S/32S isotopic ratios. Results. We report on the first detection of the doubly heavy isotopologue 12C34S2 in a comet. All three derived 34S/32S ratios yield consistent results, with δ34S values ranging from −69.91‰ ± 42.75‰ to −5.49‰ ± 51.43‰. These are within 1 to 2σ of the ViennaCanyon Diablo Troilite (V-CDT) standard, indicating at most a minor depletion in 34S. In contrast to the strong mass-dependent fractionation in water isotopologues measured on 67P - a D2O/HDO-to-HDO/H2O ratio of 17, which is far above the equilibrium value of 0.25 - our CS2 isotopologue double ratio yields 0.2377 ± 0.0139, consistent within 1σ of the statistically expected value of 0.25.