The chain polymerization in a monomolecular layer of unsaturated organic compounds on a surface is investigated using a scanning tunneling microscope (STM). We used self-ordered layers of 10,12-pentacosadiynoic acid or 10,12-nonacosadiynoic acid of diacetylene compounds on a graphite substrate. Ultraviolet light irradiation on the molecular layer induced the chain polymerization, and the created polymers can be clearly imaged by STM. The tunneling electrons from an STM tip can also excite a molecule, and the excited molecule initiates the extended chain reaction. The termination of chain reaction can also be controlled by making an artificial defect in advance using an STM tip. As a result, we can control the initiation and termination of chain polymerization with a spatial precision of the order of 1 nm.