Chalcocite is the most important and abundant secondary copper ore in the world with a rapid dissolution of copper in an acid-chloride environment. In this investigation, the methodology of surface optimization will be applied to evaluate the effect of three independent variables (time, concentration of sulfuric acid and chloride concentration) in the leaching of pure chalcocite to extract the copper with the objective of obtaining a quadratic model that allows us to predict the extraction of copper. The kinetics of copper dissolution in regard to the function of temperature is also analyzed. An ANOVA indicates that the linear variables with the greatest influence are time and the chloride concentration. Also, the concentration of chloride-time exerts a significant synergic effect in the quadratic model. The ANOVA indicates that the quadratic model is representative and the R2 value of 0.92 is valid. The highest copper extraction (67.75%) was obtained at 48 h leaching under conditions of 2 mol/L H2SO4 and 100 g/L chloride. The XRD analysis shows the formation of a stable and non-polluting residue; such as elemental sulfur (S0). This residue was obtained in a leaching time of 4 h at room temperature under conditions of 0.5 mol/L H2SO4 and 50 g/L Cl−.