Oxidative stress is the cause of numerous diseases in humans; therefore, there has been a continuous search for novel antioxidant molecules. Fungal chitosan is an attractive molecule that has several applications (antifungal, antibacterial, anticancer and antiparasitic action) owing to its unique characteristics; however, it exhibits low antioxidant activity. The aim of this study was to obtain fungal chitosan (Chit-F) from the fungus Rhizopus arrhizus and synthesize its derivative, fungal chitosan-gallic acid (Chit-FGal), as a novel antioxidant chitosan derivative for biomedical use. A low molecular weight Chi-F (~3.0 kDa) with a degree of deacetylation of 86% was obtained from this fungus. Chit-FGal (3.0 kDa) was synthesized by an efficient free radical-mediated method using hydrogen peroxide (H2O2) and ascorbic acid. Both Chit-F and Chit-FGal showed similar copper chelating activities; however, Chit-FGal was more efficient as an antioxidant, exhibiting twice the total antioxidant capacity than Chi-F (p < 0.05). Furthermore, H2O2 (0.06 M) promoted a 50% decrease in the viabilities of the 3T3 fibroblast cells. However, this effect was abolished in the presence of Chit-FGal (0.05–0.25 mg/mL), indicating that Chit-FGal protected the cells from oxidative damage. These results suggest that Chit-FGal may be a promising agent to combat oxidative stress.