In this study, a strategy was proposed for making galacto-oligossaccharides (GOS), a high value-added product, from a byproduct of the dairy industry, cheese whey, using a commercial ${eta}$-galactosidase from Kluyveromyces lactis (Lactozym$^{(R)}$ 3000L). The effects of the substrate concentration, temperature, and enzyme dosage were statistically studied and their optimum combinations were determined using response surface methodology. The increase in lactose concentration, temperature, and enzyme concentration favored a transgalactosylation reaction. The maximum values for GOS concentration (119.8 mg/mL) and yield (29.9%) in a 4 h process were obtained in the reaction system, composed of 400 mg/mL of lactose and 10 U/mL of enzyme at $40^{circ}C$. Under these conditions, the lactose conversion was 68.7%. The maximum value for lactose conversion (87.8%) was observed at the same temperature and enzyme concentration, although the lactose level was 20%.