Spallation cross sections for the reaction Ar-40(p, 2p3n)Cl-36 are measured in the energy range 47-1000 MeV. The results are used to calculate the production of cosmogenic Cl-36 on atmospheric argon by solar protons and by galactic cosmic rays. The dependence of the fall-out rate of atmospheric cosmogenic Cl-36 on geomagnetic latitude and solar activity is calculated.