Single-ion conducting polymer electrolytes represent the ideal solution to reduce concentration polarization in lithium metal batteries (LMBs). This paper reports on the synthesis and characterization of single-ion ABA triblock copolymer electrolytes comprising PEO and poly(lithium 1-[3-(methacryloyloxy)propylsulfonyl]-1-(trifluoromethylsulfonyl)imide) blocks, poly(LiMTFSI). Block copolymers are prepared by reversible addition-fragmentation chain transfer polymerization, showing low glass transition temperature (−55 to 7 °C) and degree of crystallinity (51–0%). Comparatively high values of ionic conductivity are obtained (up to ≈ 10−4 S cm−1 at 70 °C), combined with a lithium-ion transference number close to unity ( t L i + ≈ 0.91) and a 4 V electrochemical stability window. In addition to these promising features, solid polymer electrolytes are successfully tested in lithium metal cells at 70 °C providing long lifetime up to 300 cycles, and stable charge/discharge cycling at C/2 (≈100 mAh g−1).