Summary: The title polymers, in which both the stem and the graft are biodegradable, have been synthesized for the first time in a one‐pot, lipase‐catalyzed, graft‐polymerization reaction (in bulk, at 70 °C) of β‐butyrolactone (β‐BL) and ε‐caprolactone (ε‐CL) onto chitin and chitosan. The reactivity order of the lactones was found to be ε‐CL > β‐BL ≫ γ‐BL (no reaction). All the graft polymers prepared are insoluble in common organic solvents.Synthesis of chitin‐ or chitosan‐graft‐aliphatic polyesters.imageSynthesis of chitin‐ or chitosan‐graft‐aliphatic polyesters.