The ground-state rotational spectra of the six isotopomers 16O12C⋯79Br35Cl, 16O12C⋯81Br35Cl, 16O12C⋯79Br37Cl, 16O12C⋯81Br37Cl, 16O13C⋯79Br35Cl, and 16O13C⋯81Br35Cl, of a dimer formed by carbon monoxide and bromine monochloride have been observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The rotational constant B0, the centrifugal distortion constant DJ and the halogen nuclear quadrupole coupling constants χaa(X), where X = Cl or Br, have been interpreted to give the properties of the weakly bound complex. It was found that the molecule is linear and has the arrangement OC⋯BrCl, with the Br atom forming the intermolecular bond to carbon. Values of the rs type for the distances r(C⋯Br) and r(BrCl) have been derived and the limitations imposed on these by the small coordinate aBr are considered. The effect of bond shrinkage resulting from isotopic substitution at Br indicates that the rs value of aBr is underestimated and it is concluded that there is probably only a small increase in r(BrCl) on formation of the complex. An interpretation of the χaa(X) values indicates that the electric charge distribution in BrCl is also only slightly perturbed.