We applied infrared matrix isolation spectroscopy to investigate the reactions between Cl atom and acetylene (C₂H₂) in a para-hydrogen (p-H₂) matrix at 3.2 K; Cl was produced via photodissociation at 365 nm of matrix-isolated Cl₂ in situ. The 1-chloroethyl radical (·CHClCH₃) and chloroethene (C₂H₃Cl) are identified as the main products of the reaction Cl + C₂H₂ in solid p-H₂. IR absorption lines at 738.2, 1027.6, 1283.4, 1377.1, 1426.6, 1442.6, and 2861.2 cm⁻¹ are assigned to the 1-chloroethyl radical. For the reaction of Cl + C₂D₂, lines due to the ·CDClCH₂D radical and trans-CHDCDCl are observed; the former likely has a syn-conformation. These assignments are based on comparison of observed vibrational wavenumbers and ¹³C- and D-isotopic shifts with those predicted with the B3LYP/aug-cc-pVDZ and MP2/aug-cc-pVDZ methods. Our observation indicates that the primary addition product of Cl + C₂H₂, 2-chlorovinyl (·CHCHCl) reacts readily with a neighboring p-H2 molecule to form ·CHClCH₃ and C₂H₃Cl. Observation of ·CDClCH₂D and trans-CHDCDCl from Cl + C₂D₂ further supports this conclusion. Although the reactivity of p-H₂ appears to be a disadvantage for making highly reactive free radicals in solid p-H₂, the formation of 1-chloroethyl radical indicates that this secondary reaction might be advantageous in producing radicals that are difficult to prepare from simple photolysis or bimolecular reactions in situ.