Organometallic-mediated chain growth polymerization of readily accessible chemical building blocks is responsible for important commercial and technological advances in polymer science, but the incorporation of heteroatoms into the polymer backbone through these mechanisms remains a challenge. Transition metal π-allyl complexes are well-developed organometallic intermediates for carbon-heteroatom bond formation in small-molecule catalysis yet remain underexplored in polymer science. Here, we developed a regioselective palladium-phosphoramidite-catalyzed chain-growth allylic amination polymerization of vinyl aziridines for the synthesis of novel nitrogen-rich polymers via ambiphilic π-allyl complexes. The polymerization accessed a linear microstructure with four carbons between each nitrogen, which is challenging to achieve through other chain-growth polymerization approaches. The highly regioselective allylic amination polymerization demonstrated the characteristics of a controlled polymerization and was able to achieve molar masses exceeding 20 kg mol-1 with low dispersities (D̵ < 1.3). The identification of the polymer structure and well-defined chain ends were supported by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry, and chain extension experiments demonstrate opportunities for building more complex materials from this method. A Hammett study was performed to understand the role of the catalyst and monomer structure on regioselectivity, and the data supported a mechanism wherein regioselectivity was primarily controlled by the ligand-metal complex. Postpolymerization desulfonylation provided access to a novel polyamine that demonstrated broad anticancer activity in vitro, which highlights the benefits of unlocking novel polyamine microstructures through regioselective chain-growth allylic amination polymerization.