We explore the third-order optical nonlinear properties of arsenic- and germanium-free chalcogenide glasses (ChGs) within a gallium-tin-selenium (Ga-Sn-Se, GSS) ternary system at wavelength of 1.064 mu m in the picosecond region. A classical characterization showing the values of the absorption and the linear index will be given. Then, using D4 sigma-Z-scan technique, both nonlinear refractive index (n(2)) and nonlinear absorption coefficient (beta) of the GSS ChGs will be measured. A comparison of the results is made with other families of chalcogenide glasses considering the figure of merit calculation. The first results show that GSS system would give better NL performance promising high potential for n(2)(beta)-based photonic devices performed under clean production and green/sustainable chemistry.