(U)B3LYP Calculations with the 6-31+G(d) and 6-311+G(2df) basis sets have been carried Out Oil cyclooctatetraenes 6 and 7, in which the COT ring is tetrakis-annelated with alpha-dithio- or alpha-diselenocarbonyl groups. Transferring two electrons from the high-lying b(1g) and e(u) sigma MOs in 6 and 7 into the unoccupied, nonbonding, COT pi orbital is computed to be energetically favorable. The lowest D-4h, electronic state is Calculated to be E-3(u) which formally contains 10 T. electrons in the eight-membered ring and has two unpaired electrons in a MOs. The E-3(u) state undergoes a first-order Jahn-Teller distortion to form 6d and 7d, in which the pair of one-electron holes in the sigma MOs is stabilized by the formation of two, two-center, three-electron bonds between pairs of chalcogen atoms that are diagonally across the eight-membered ring from each other. The corresponding open-shell singlets are computed to be about 1 kcal/mol lower in energy than the Jalin-Teller distorted triplets. Molecules 6i and 7i, in which the C-C bond in one four-membered ring is cleaved, are computed to be lower in energy than 6d and 7d. However, a Substantial barrier is predicted to sepal-ate each of the two pairs of isomers so that 6d and 7d should, at least in principle, be isolable.