The electrical characterization of single-polymer chains on a surface is an important step towards novel molecular device development. The main challenge is the lack of appropriate atomically flat insulating substrates for fabricating single-polymer chains. Here, using atomic force microscopy, we demonstrate that the (0001) surface of an insulating hexagonal boron nitride (h-BN) substrate leads to a flat-lying self-assembled monolayer of diacetylene compounds. The subsequent heating or ultraviolet irradiation can initiate an on-surface polymerization process leading to the formation of long polydiacetylene chains. The frequency of photo-polymerization occurrence on h-BN(0001) is two orders of magnitude higher than that on graphite(0001). This is explained by the enhanced lifetime of the molecular excited state, because relaxation via the h-BN is suppressed due to a large band gap. We also demonstrate that on-surface polymerization on h-BN(0001) is possible even after the lithography process, which opens up the possibility of further electrical investigations.