Pure rotational transitions of the ClSO radical have been observed by Fourier-transform microwave spectroscopy. a-type and b-type transitions, for both 35Cl and 37Cl isotopologues, were detected, and the observed very complicated fine and hyperfine components were assigned well. The intensities of the observed spectra of the two isotopologues correspond to the ratio of the isotope abundances of 35Cl and 37Cl. A total of 21 molecular constants were determined precisely for both 35ClSO and 37ClSO, including the rotational constants, centrifugal distortion constants, electronic spin-rotation constants, nuclear spin-rotation constants, magnetic hyperfine constants, and quadrupole coupling constants of chlorine. The molecular constants show ClSO to have the 2A'' electronic ground state with an out-of-plane unpaired electron. The spin density of the chlorine atom is about 10.6%, which is similar to that of the fluorine atom for FSO, about 8%. Results of the ClSO radical are compared with those of other triatomic radicals with similar structures, the XSS, XSO, and XOO radicals with X = H, F, and Cl, leading to a conclusion that the ClSO radical is more like FSO, but fairly different from the FOO and ClOO radicals.