Generation of third harmonic of CO₂ laser radiation has been obtained in a type-II, ϑ=57° cut 9 mm thick AgGaSe₂ crystal for the first time by sum-frequency-mixing of the fundamental with its second harmonic, the latter being obtained using another type-I, ϑ=55° cut 11 mm thick AgGaSe₂ crystal. The energy conversion efficiencies obtained for second harmonic and third harmonic generations are 6.3% and 2.4% respectively with the input fundamental pump power density of 5.9 MW/cm² only. The wavelength of the fundamental CO₂ laser radiation used for the generation of harmonics is 10.6 µm, P(20) line. A compact TEA CO₂ laser source has been built in the laboratory.