By-products from the industrialization of oilseeds, particularly chia, can be sustainably used for the development of new functional products. In this work, wheat breads supplemented with up to 10 mg of chia expeller hydrolysate/g of flour were prepared, obtaining fortified breads with acceptability for consumption, according to a preliminary consumer research study based on an affective test employing a five-point hedonic scale of global acceptance. In this context, protein hydrolysates of the chia expeller were produced using Alcalase, reaching a degree of hydrolysis of 54.3 ± 1.6% with an antioxidant activity of 55.8 ± 0.4% after 6 h incubation at 25 °C in the presence of the enzyme. These peptides showed appropriate techno-functional properties and chemical compositions suitable for the further development of bakery products. Taken together, our approach and the development of a fortified bread with plant-based bioactive peptides provide a novel and eco-friendly alternative for the recovery of nutrients from agro-industrial waste. More importantly, these enriched breads could exert beneficial effects on human health by exploiting the antioxidant properties of functional peptides derived from the chia expeller.