The Cu-based chalcopyrite compounds are good thermoelectrics for waste heat harvesting, partially due to the dramatic reduction of the thermal conductivity above Debye temperature, whereas the mechanism of this drop is still elusive. By Raman measurements from 7 to 780 K, we have investigated the anharmonicity of the phonon modes B12, A1, and B32 in CuInTe2. The fourth-order anharmonicity of B12 and B32 modes is greatly enhanced with increasing temperature and becomes dominant above 400 K. The phonon dynamics is calculated from 10 to 800 K. The fourth-order anharmonicity is predominant over the third-order ones for the phonon modes at low ( 70 cm???1) and high ( 130 cm???1) frequency domains, confirmed by the enhanced weighted phase space and scattering rate of the four-phonon processes above 300 K. The phonon avoided-crossing is found to take place around 40 cm???1 between the lowest-optical mode and acoustic modes. Counting on the fourth-order phonon anharmonicity, the calculated lattice thermal conductivity agrees well with experiment. The results unveil that the dramatic thermal conductivity reduction, about 83% from 300 to 800 K, originates from the enhanced four-phonon process. Our insights on the thermal transport mechanisms might benefit the materials design of thermoelectrics and thermal control.