A detailed study of the neutron-capture gamma-ray spectrum for chlorine, above an energy of 1.6 MeV, has revealed a total of 234 transitions with intensity greater than 0.04%. Consistency tests indicate that the average energy uncertainty for the entire set of gamma rays is 0.1 keV. Data reduction was accomplished by invoking spectral deconvolution techniques with the result that many previously reported transitions were found to be multiplets. A decay scheme was derived by making use of both these new findings and the high energy precision attained for the transition energies. The proposed decay scheme accounts for more than 98% of the observed intensity and the energy of the levels included were found to have an average uncertainty of 0.08 keV. Based upon an error-free 15N neutron separation energy of 10 833.30 keV, the Q values for 35Cl(n,γ)36Cl and 37Cl(n,γ)38Cl were found to be 8579.82 (2) and 6107.85 (10) keV, respectively.