We demonstrate a controllable surface-coordinated linear polymerization of long-chain poly(phenylacetylenyl)s that are self-organized into a "circuit-board" pattern on a Cu(100) surface. Scanning tunneling microscopy/spectroscopy (STM/S) corroborated by ab initio calculations, reveals the atomistic details of the molecular structure, and provides a clear signature of electronic and vibrational properties of the poly(phenylacetylene)s chains. Notably, the polymerization reaction is confined epitaxially to the copper lattice, despite a large strain along the polymerized chain that subsequently renders it metallic. Polymerization and depolymerization reactions can be controlled locally at the nanoscale by using a charged metal tip. This control demonstrates the possibility of precisely accessing and controlling conjugated chain-growth polymerization at low temperature. This finding may lead to the bottom-up design and realization of sophisticated architectures for molecular nano-devices.