We developed a new approach to obtain polylactide hybrid block copolymers with vinyl monomers (styrene, methyl methacrylate, methyl acrylate) through the realization of a reaction sequence using triethylborane and various p-quinones. The method offered includes two stages. In the first stage, a chain-transfer agent was obtained by borylation of the terminal hydroxyl groups of polylactide. The second stage was vinyl monomer radical polymerization in the presence of p-quinone accompanied by S H 2-substitution at the boron atom.1,4-Naphthoquinone, 2,3-dimethyl-1,4-benzoquinone, duroquinone and 2,5-di-tert-butyl-1,4-benzoquinone were used as synthetic polymer chain growth mediators. It is shown that 1,4-naphthoquinone and 2,3-dimethyl-1,4-benzoquinone, similar in their characteristics, are effective agents providing the realization of reversibledeactivation radical polymerization. Realization of reversible-deactivation radical polymerization was proved with the analysis of the kinetics of block copolymerization, molecular weight characteristics and compositional homogeneity of block copolymers as well as its further capability to elongate the polymer chain. Synthesized block copolymers have a high thermal stability compared to the initial borylated polylactide.