Living covalent polymerization has been a subject of intense research for many decades and has culminated in the synthesis of a large variety of block copolymers (BCPs) with structural and functional diversity. In contrast, the research on supramolecular BCPs is still in its infancy and their generation by living processes remains a challenge. Here we report the formation of supramolecular block copolymers by two-component seeded living polymerization of properly designed perylene bisimides (PBIs) under precise kinetic control. Our detailed studies on thermodynamically and kinetically controlled supramolecular polymerization of three investigated PBIs, which contain hydrogen-bonding amide side groups in imide position and chlorine, methoxy, or methylthio substituents in 1,7 bay-positions, revealed that these PBIs form kinetically metastable H-aggregates, which can be transformed into the thermodynamically favored J-aggregates by seed-induced living polymerization. We show here that copolymerization of kinetically trapped states of one PBI with seeds of another PBI leads to the formation of supramolecular block copolymers by chain-growth process from the seed termini as confirmed by UV/vis spectroscopy and atomic force microscopy (AFM). This work demonstrates for the first time the formation of triblock supramolecular polymer architectures with A-B-A and B-A-B block pattern by alternate two-component seeded polymerization in a living manner.