Nanoindentation is used to study the mechanical properties at the nanoscale of the ternary Agx(As0.33S0.67)100-x glassy system for 0 ≤ x ≤ 25. Direct evidence for phase separation of a Ag-poor and a Ag-rich phase in the composition range 2 ≤ x ≤ 20 is provided. The volume of the Ag-rich phase increases with x and percolates at x ≈ 7. The mechanical properties of the Ag-rich phase are comparable to those of the x = 25 glass, while those of the Ag-poor phase are closer to (however, quite different from) the ones of the base glass AsS2. The structure of both phases at short and medium range order is investigated by micro-Raman spectroscopy and is correlated to their mechanical properties.