We have studied the mechanism of photoinduced chain polymerization in the self-assembled monolayer of a diacetylene compound, 10,12-pentacosadiyn-1-ol, on the graphite surface. We statistically analyze the polymerization degree of the polydiacetylene chains formed at different temperatures using scanning tunneling microscopy. The distributions of the polymerization degree agree well with the prediction from a simple probabilistic model, allowing for addition reaction and deactivation at both the ends of the chain as stochastic events. The estimated activation energies of the addition reaction and deactivation are noticeably different from those of the conventional solid-state polymerization in the bulk crystals of diacetylene.