We report theoretical studies on oxygen excess defect structure of lanthanum cuprate, La2CuO4+δ, using the Local Density formalism. The self-consistent Discrete Variational method has been used to find energy levels, densities of states, charge transfer, wavefunctions and potentials for a fragment consisting of N atoms embedded in the infinite crystal. Various possible interstitial oxygen positions and relative stability have been studied, including the structure suggested by Chaillout, et al. on the basis of neutron diffraction. Calculated electronic structures have been used to predict defect-related spectroscopic consequences.