Electronic band structure computations for a perfect hexagonal layer of CBN have been performed via density functional theory using the local density approximation to the exchange-correlation potential. A small band gap of 0.2 eV is thereby obtained, with the band gap being offset away from the central -point of the two-dimensional Brillouin zone. These results are rationalized in terms of a simple empirical Hckel model, for which simple structural criteria for a zero band gap are noted. Special attention is paid to the case with a minimum content of carbon, and some comparison is made to earlier band structures for two different geometrical layers of C2BN. 1998 Elsevier Science Ltd. All rights reserved.