Tacticity is a crucial factor affecting the properties of synthetic polymer materials. Here, we introduce a type of chiral organic Brønsted acid catalyst, 1,1'-bi-2-naphthol-derived N,N'-bis(triflyl)phosphoramidimidates (PADIs), for the cationic polymerization of vinyl ethers, which enables the development of the first organocatalytic, highly stereoselective, cationic reversible addition-fragmentation chain-transfer (RAFT) polymerization of vinyl ethers with a trithiocarbonate chain-transfer agent. This metal-free RAFT process could afford isotactic poly(vinyl ethers) with high stereoselectivity, controllable molecular mass, and narrow dispersity at low catalyst loadings (as low as 200 ppm). Moreover, the trithiocarbonate chain-end allows for chain extension to synthesize diblock copolymers comprising an isotactic poly(vinyl ether) block, by a mechanistic switching from stereoselective cationic RAFT polymerization to visible-light-regulated cationic and radical RAFT polymerization.