In this study ESR, UV, VIS and IR spectroscopy, 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 vinyl monomer acrylamide. These radicals are able to initiate chain reaction of polymerization of monomers at low temperatures. This reaction results in a completely soluble polymer with a yield of 25 %, 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 <$Esymbol Ы~1~%> while the overall yield was <$Esymbol Ы~10~%>. p-Diethynylbenzene polymerizes at temperatures close to chlorine melting (170 K). Polymerization of acrylamide takes place in the temperature range of 180 - 210 K with an yield of polymer <$Esymbol Ы~10~%>. 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.