Poly(lactic acid) (PLA) is a biodegradable polymer prepared by the catalyzed ring opening polymerization of lactide. An ideal catalyst should enable a sequential polymerization of the lactide enantiomers to afford stereoblock copolymers with predetermined number and lengths of blocks. We describe a magnesium based catalyst that combines very high activity with a true-living nature, which gives access to PLA materials of unprecedented microstructures. Full consumption of thousands of equivalents of L-LA within minutes gave PLLA of expected molecular weights and narrow molecular weight distributions. Precise PLLA-b-PDLA diblock copolymers having block lengths of up to 500 repeat units were readily prepared within 30 min, and their thermal characterization revealed a stereocomplex phase only with very high melting transitions and melting enthalpies. The one pot sequential polymerization was extended up to precise hexablocks having "dialed-in" block lengths.