In this study, ESR, UV, VIS and IR spectroscopy, as well as chromatography, calorimetry, and elemental analysis were employed to show the spontaneous formation of free radicals under low-temperature action of molecular chlorine on acetylene monomer p-diethynylbenzene and on vinyl monomer acrylamide. These radicals are able to initiate a chain reaction of polymerization of monomers at low temperatures. This reaction results in a completely soluble polymer with a 25% yield, while an insoluble cross-linked polymer has been obtained during polymerization of p-diethynylbenzene initiated by other means. For example, under radiolysis by 1000 kGy the soluble fraction of obtained polymer was ≈1%, while the overall yield was ≈10%. p-Diethynylbenzene polymerizes at temperatures close to the melting temperature of chlorine (170 K). Polymerization of acrylamide takes place in the temperature range of 180–210 K with a ≈10% yield of polymer. The low-temperature chlorination of a 20% solution of acrylamide in glycerol enables a twofold increase of the polymer yield and a tenfold decrease of the chlorine content in it.