"Click" chemistry is a powerful method for post-polymerization modification of polymers and other materials. Because of the importance of lactide-based functional polymers in materials and medical applications, we synthesized 3,6-dipropargyl-1,4-dioxane-2,5-dione, an acetylene-functionalized glycolide monomer. Its subsequent polymerization and copolymerization with lactide provided a new polyglycolide homopolymer as well as random and block copolymers that have pendant acetylene groups available for the attachment of chemical functionality using "click" chemistry. A protocol was devised to permit "click" functionalization of polyglycolides with no degradation in molecular weight. As one demonstration of the power of this approach to substituted polyglycolides, we have prepared a family of degradable, thermoresponsive materials that exhibit lower critical solution temperatures (LCST) from room temperature to > 60 degrees C.