The Peierls instability in chain-like substances is reexamined and a two-step Peierls transition theory is developed. The weak inter-chain coupling makes the CDW transition and the associated metal-insulator transition occur at different temperatures and allows the CDW to coexist with the metallic feature. The resistivity anomaly in TaS₃ between 215 and 270 K and the pressure-induced metal-insulator transition in (DMe-DCNQI)₂Cu are well explained.