Chitin and chitosan, valuable marine biopolymers, recovered from shrimp waste, are an abundant by-product of the shrimp processing industry in Vietnam, at an estimated 200000 metric tons per year. The obtained chitin and chitosan are characterized by their purity and functional properties. The polymers show good quality with low residual ash and protein content (<1%). The antioxidant potency of chitosan is evaluated by several different in vitro systems, including 1,1-diphenyl-2-picrylhydrazyl (DPPH) free radical scavenging, total reducing power, and inhibition of lipid peroxidation. The DPPH free radical scavenging, total reducing power, and lipid peroxidation inhibition activities of chitosan at varying concentration (0.125 to 1.0 mg/mL) range from 3.7 to 16.8%, 0.05 to 0.15, and 1.7 to 15.1%, respectively. This study demonstrates that chitin and chitosan, of good quality and having characteristics compatible with a broad range of applications, can be prepared from white shrimp waste.