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The total photoionization cross section of the 3p subshell of atomic chlorine is presented with use of the recently developed open-shell transition-matrix method of Starace and Shahabi. The role of electron correlations is studied by comparison with Hartree-Fock and close-coupling calculations. In contrast to 3p-subshell photoionization of argon, it is shown that, in chlorine, final-state interchannel interactions are very strong while virtual pair excitations have a weak effect on the shape of the cross section, serving mainly to reduce the discrepancy between length and velocity results. Our results are compared in detail with other theoretical results above the 1S threshold as well as with experimental relative-intensity measurements at 584 Å. While our results are lower than the others at the 1S threshold (ℏω=0.6 a.u.), at photon energies ℏω>1 a.u., our geometric mean cross section is in essentially exact agreement with unrelaxed ionic core results of Brown, Carter, and Kelly and of Fielder and Armstrong.