The authors have investigated the electronic structure of the non-superconducting compound YBa2Cu3O6. They find the compound to be metallic with a somewhat reduced density of states (DOS) at the Fermi level, as compared with its sister superconducting compound YBa2Cu3O7. The structure in the DOS at the pyramidally coordinated copper site and the four oxygen atoms which form a square planar configuration around it are not substantially modified in YBa2Cu3O6 relative to YBa2Cu3O7. But the absence of linear chain oxygen atoms transforms the associated copper atoms into Cu+ and the oxygen atom with which this Cu interacts becomes almost ionic in nature, with vanishingly small DOS at the Fermi level at both sites. It thus appears that the Cu-O linear chains play an important role in superconductivity in YBa2Cu3O7.