The chemical modification of polylactic acid (PLA) and related polyesters by peroxide-initiated grafting of multifunctional allylic and acrylic monomers is described. Solvent-free, melt-state reactions of PLA and triallyl trimesate (TAM) are shown to be remarkably efficient compared to analogous reactions of polyolefins such as poly(ethylene-co-octene) (EOC), requiring very low reagent loadings to produce a long chain branched (LCB) architecture. A systematic study of potential transesterification chemistry confirms that ionic reactions do not contribute significantly to PLA reactivity under typical grafting conditions. Further explorations of H-atom abstraction and monomer addition yields demonstrate that PLA is relatively unreactive toward the radical reactions that support LCB production. Careful examination of the solubility of coagent intermediates reveal dramatic differences in oligomer solubility between a hydrocarbon system and an ester-based matrix. Whereas TAM conversion in hydrocarbon leads to a precipitation polymerization that removes coagent from solution, reactions conducted in the polyester do not incur losses of oligomeric intermediates, indicating that the ability of PLA to retain multi-functional intermediates is the underlying cause of its remarkable LCB grafting yields.