We have examined by high-level calculations the electronic structure of the recently isolated chiral fullerene molecule C 76 (R. Ettl, I. Chao, F. Diederich and R.L. Whetten, Nature 353 (1991) 149. The relaxed structure maintains D 2 symmetry and has near-ideal bonding angles and lengths for fullerene structures. The electronic density-of-states is dominated by pπ orbitals near the Fermi energy, where it closely resembles the naive tight-binding (Hückel) pattern. The calculated low-energy optical spectrum, and the small HOMO—LUMO gap (1.1 eV) in particular, are in agreement with experiment, and allow for a detailed interpretation of observed near-infrared spectral bands, in terms of four allowed transitions. The vertical ionization potential (8.1 eV) and electron affinity (2.9 eV) are also predicted.