We have analyzed and evaluated Cl-35, Cl-37, and Cl-nat neutron cross section data in the resolved resonance region with the multilevel Reich-Moore R-matrix formalism. Energies and widths were determined for 388 resonances in the range 0.2 to 1200 keV. New J assignments were made for 33 resonances, and parities were assigned for 15 of these resonances. Neutron strength functions were calculated for both s and p waves; our results include the first reported p-wave values for Cl. Resonance analyses were carried out with the computer code SAMMY, which utilizes Bayes' method, a generalized least-squares technique. Because SAMMY now has the ability to calculate charged-particle penetrabilities, it was possible to include a proton exit channel in the analysis and to deduce proton widths for several resonances. Our resonance parameter representation describes the data much better than previous evaluations, and it should lead to improved criticality safety calculations for systems where Cl is present.