We report infrared spectroscopic studies of H₂ ortho-para (o/p) conversion in solid hydrogen doped with Clatoms at 2 K while the Cl+H₂(v=1)→HCl+H infrared-induced chemical reaction is occurring. The Cl-atom doped hydrogen crystals are synthesized using 355 nm in situ photodissociation of Cl₂ precursor molecules. For hydrogen solids with high ortho-H₂ fractional concentrations (Xo=0.55), the o/p conversion kinetics is dominated by Cl-atom catalyzed conversion with a catalyzed conversion rate constant Kcc=1.16(11) min⁻¹ and the process is rate-limited by ortho-H₂ quantum diffusion. For hydrogen crystals with low ortho-H₂ concentrations (Xo=0.03), single-exponential decay of the ortho-H₂ concentration with time is observed which is attributed to H-atom catalyzed o/p conversion by the H-atoms produced during the infrared-induced Cl+H₂ reaction. The measured H-atom catalyzed o/p conversion kinetics indicates the H-atoms are mobile under these conditions in agreement with previous ESR measurements.