In contrast to allyl palladium complexes, propargylic/allenylic palladium species display complex reactivities that limit their implementation in polymer chemistry, especially for chain-growth polymerizations. Here we report an example of controlled chain-growth polymerization via propargyl/allenyl palladium intermediates. Vinylidenecyclopropane 1,1-dicarboxylate (VDCP), a unique allenylic electrophile, selectively reacts via the σ-allenyl palladium complex rather than the more common π-propargyl pathway, thereby unlocking a chain-growth process. Based on this concept, precise synthesis of alkyne-backbone polymers is realized, featuring fast rate, high molecular weight, narrow dispersity, high chemoselectivity, and excellent end-group fidelity. We demonstrate preparation of unsaturated macromolecules with advanced sequences and architectures using this method, including block, gradient, and graft copolymers.