Understanding the nature of phonon transport in solids and the underlying mechanism linking lattice dynamics and thermal conductivity is important in many fields, including the development of efficient thermoelectric materials where a low lattice thermal conductivity is required. Herein, we choose the pair of synthetic chalcopyrite CuFeS2 and talnakhite Cu17.6Fe17.6S32 compounds, which possess the same elements and very similar crystal structures but very different phonon transport, as contrasting examples to study the influence of lattice dynamics and chemical bonding on the thermal transport properties. Chemically, talnakhite derives from chalcopyrite by inserting extra Cu and Fe atoms in the chalcopyrite lattice. The CuFeS2 compound has a lattice thermal conductivity of 2.37 W m-1 K-1 at 625 K, while Cu17.6Fe17.6S32 features Cu/Fe disorder and possesses an extremely low lattice thermal conductivity of merely 0.6 W m-1 K-1 at 625 K, approaching the amorphous limit κmin. Low-temperature heat capacity measurements and phonon calculations point to a large anharmonicity and low Debye temperature in Cu17.6Fe17.6S32, originating from weaker chemical bonds. Moreover, Mössbauer spectroscopy suggests that the state of Fe atoms in Cu17.6Fe17.6S32 is partially disordered, which induces the enhanced alloy scattering. All of the above peculiar features, absent in CuFeS2, contribute to the extremely low lattice thermal conductivity of the Cu17.6Fe17.6S32 compound.