Doping in a lattice refers to the introduction of very small quantities of foreign atoms and has a generally small effect on decreasing the lattice thermal conductivity, unlike alloying which involves large fractions of other elements and strongly enhances point defect phonon scattering. Here, we report that, by alloying only 3% of In on the Cu sites of the diamond-like lattice of CuFeS2 chalcopyrite compound (Cu1-xInxFeS2, x = 0.03) has a disproportionally large effect in reducing the lattice thermal conductivity of the compound from 2.32 to 1.36 Wm(-1)K(-1) at 630 K. We find that In is not fully ionized to +3 when on the Cu sublattice and exists mainly in the +1 oxidation state. The 5s(2) lone pair of electrons of In+ makes this atom incompatible (referred to as discordant) with the tetrahedral geometry of the crystallographic site. This causes strong local bond distortions thereby softening the In-S and Cu-S chemical bonds and introducing localized low frequency vibrations. The latter couple with the base phonon frequencies of the CuFeS2 matrix enhancing the anharmonicity and decreasing the phonon velocity, and consequently the lattice thermal conductivity. The control material in which the In doping is on the Fe3+ site of the structure at the same doping level (and found in the site-compatible In3+ state), has a far smaller effect on the phonon scattering.