We present results of a study of neutrino oscillation based on a 766 ton/year exposure of KamLAND to reactor antineutrinos. We observe 258 nu (e) candidate events with energies above 3.4 MeV compared to 365.2+/-23.7 events expected in the absence of neutrino oscillation. Accounting for 17.8+/-7.3 expected background events, the statistical significance for reactor nu (e) disappearance is 99.998%. The observed energy spectrum disagrees with the expected spectral shape in the absence of neutrino oscillation at 99.6% significance and prefers the distortion expected from nu (e) oscillation effects. A two-neutrino oscillation analysis of the KamLAND data gives Deltam(2)=7.9(+0.6)(-0.5)x10(-5) eV(2). A global analysis of data from KamLAND and solar-neutrino experiments yields Deltam(2)=7.9(+0.6)(-0.5)x10(-5) eV(2) and tan((2)theta=0.40(+0.10)(-0.07), the most precise determination to date.