[ $ZnHgGa_4Se_8;and;ZnHgGa_4Se_8::Co^{2+}$ ] single crystals were grown by the Bridgman-Stockbarger method. The single crystals crystallized into a defect chalcopyrite structure. The optical energy band gap of the single crystals was investigated in the temperature range 11-300K. The optical energy band gap of the $ZnHgGa_4Se_8:Co^{2+}$ single crystal was smaller than that of the $ZnHgGa_4Se_8$ single crystal. The temperature dependence of the optical energy band gap of the single crystals was well fitted by the Varshni equqtion. The impurity optical absorption spectrum of the $ZnHgGa_4Se_8:Co^{2+}$ single crystal was measured in the wavelength region 300-2300 m at 80 K. Impurity absorption peaks in the spectrum were analyzed within the framework of the crystal field theory and were attributed to the electron transitions between the energy levels of $Co^{2+}$ sited in the Td symmetry point.