Carbon-13 CP/MAS NMR spectra of two closely related solid chloroketosulfones have been examined. Peaks arising from carbon nuclei which are spatially proximate to chlorine nuclei exhibit extensive broadening and in some cases fine structure, particularly at the lower applied magnetic fields. Residual Cl-35/37-C-13 spin-spin interactions are responsible for the broadening and fine structure. By consideration of the appropriate Zeeman-quadrupolar Hamiltonian, the observed C-13 CP/MAS NMR spectra can be reproduced by exact numerical computer calculations. The excellent agreement between the observed and calculated spectra allows one to-determine both the sign and magnitude of the Cl-35/37 nuclear quadrupolar coupling constant, chi, and the Cl-35/37-C-13 indirect spin-spin coupling constant, (1)J(Cl-35/37, C-13). The values determined for the Cl-35-C-13 spin pair are chi(Cl-35) = -73 +/- 2 MHz and (1)J(Cl-35, C-13) = -20 +/- 5 Hz. This is the first direct measurement of 1J(Cl-35/37, C-13); the magnitude and negative sign of this coupling constant are consistent with known periodic trends.