The first experimental detection of an antisymmetrical component (σa) in the NMR shielding tensor of a nucleus is reported. The 13C NMR relaxation rates (1/T1 and 1/T2) of the ethylenic carbons in tetrachlorocyclopropene in toluene-d8 at about -90°C are dominated at high fields by shielding tensor modulated by random molecular rotation. We find that T2 is circa 1.1T1 in contrast to that in 13CS2, where σa is zero by symmetry and where the measured T2 is not greater than the maximum (0.857T1) allowed for this case. The present results are in qualitative agreement with previous ab initio IGLO calculations showing that the ethylenic carbons in cyclopropenes have unusually large antisymmetric components in their shielding tensors. © 1990.