We present an improved measurement of the oscillation between the first two neutrino families based on a 766.3 ton-year exposure of KamLAND to reactor anti-neutrinos. KamLAND observes 258 events with nue-bar energies above 3.4MeV compared to 365.2 events expected in the absence of neutrino oscillation. The confidence level for reactor nue-bar disappearance is now 99.995%. The observed energy spectrum disagrees with the expected spectral shape in the absence of neutrino oscillation at the 99.9% confidence level but agrees with the distortion expected from nue-bar oscillation effects. A two-neutrino oscillation analysis of the KamLAND data gives a best-fit point at DeltaMSq=8.3times10^{-5}eV^2 and tan{^2}theta=0.41. A global analysis of data from KamLAND and solar neutrino experiments yields DeltaMSq=8.2^{+0.6}_{-0.5}times10^{-5}eV^2 and tan^{2}theta =0.40^{+0.09}_{-0.07}, the most precise determination to date.