The surface properties of the Li2O2 discharge phase are expected to impact strongly the capacity, rate capability, and rechargeability of Li-oxygen batteries. Prior calculations have suggested that the presence of half-metallic surface states in Li2O2 may mitigate electrical passivation resulting from the growth of Li2O2, which is a bulk insulator. Here we revisit the electronic structure of bulk Li2O2 and the dominant Li2O2 {0001} surface by comparing results obtained with the PBE GGA functional, the HSE06 hybrid functional, and quasiparticle GW methods. Our results suggest that the bulk band gap lies between the value predicted by the G(0)W(0) method, 5.15 eV, and the value predicted by the self-consistent quasiparticle GW (scGW) approximation, 6.37 eV. The PBE, HSE06, and scGW methods agree that the most stable surface, an oxygen-rich {0001} termination, is indeed half-metallic. This result supports the notion that the electronic structure of surfaces may play an important role in understanding performance limitations in Li-oxygen batteries.