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Cu2SnS3is the parent compound of a series of phases in the Cu2+xSn1–xS3section (0 ≤ x≤ 0.15) of the ternary Cu–Sn–S phase diagram, the crystal structure of which can be controlled by varying the synthesis process and/or through a fine-tuning of the chemical composition. Despite being structurally close to the sphalerite structure, the thermal transport of these compounds is strongly dependent on the exact lattice symmetry and degree of atomic disorder. Here, we investigate the lattice dynamics of the monoclinic ordered Cu5Sn2S7(space group C2) and cubic disordered Cu5Sn2S6.65Cl0.35(space group F4̅3m) compounds by temperature-dependent powder inelastic neutron scattering (INS). In both cases, the INS spectra feature low-energy optical modes mostly weighed by the thermal motion of Cu atoms. The response of the INS spectra of Cu5Sn2S6.65Cl0.35to temperature variations is indicative of quasi-harmonic behavior. Combined with analyses of the low-temperature specific heat, these findings show that the significant lowering of the lattice thermal conductivity in cubic Cu5Sn2S6.65Cl0.35is due to a reduced phonon mean free path tied to the increased level of disorder in the unit cell. These results highlight how the stabilization of highly symmetric, yet strongly disordered crystal structures akin to those observed in high-entropy alloys, can lead to a drastic reduction in the heat transport, offering an effective approach to design high-performance thermoelectric sulfides.