The radiative association (RA) rate constant is computed for the formation of the diatomic sodium chloride (NaCl) molecule in the temperature interval 1 K–30 K. At these temperatures, RA of NaCl through non-adiabatic dynamics is important. A scattering program has been implemented to carry out calculations of RA cross sections, accounting for coupled dynamics on the lowest ionic and the lowest neutral diabatic 1Σ+ states. The study shows that the non-adiabatic treatment gives a cross section that exceeds that of conventional adiabatic dynamics by one to four orders of magnitude. The contribution to the RA rate constant from Na and Cl approaching each other in the A1Π state has also been computed using an established quantum mechanical method. Ab initio data from the literature have been used for the potential energy curves, the diabatic coupling, and the electric dipole moments of NaCl.