Twelve high-quality chia protein hydrolysates (CPHs) were produced from chia protein isolate (CPI) in a pilot plant of vegetable proteins. To obtain functional hydrolysate, four CPHs were hydrolyzed by the action of Alcalase, an endoprotease, and the other eight CPHs were hydrolyzed by the action of Flavourzyme, an exoprotease. Alcalase-obtained CPHs showed significant antihypertensive properties particularly, the CPH obtained after 15 min of hydrolysis with Alcalase (CPH15A), which showed a 36.2% hydrolysis degree. In addition, CPH15A increased the antioxidant capacity compared to CPI. The CPH15A physicochemical composition was characterized and compared to chia defatted flour (CDF) and CPI, and its techno-functional properties were determined by in vitro experiments through the analysis of its oil absorption capacity, as well as the capacity and stability of foaming and emulsifying, resulting in an emulsifier and stabilizer better than the intact protein. Therefore, the present study revealed that CPH15A has potent antihypertensive and antioxidant properties and can constitute an effective alternative to other plant protein ingredients sources that are being used in the food industry.