KamLAND has measured the flux of v̅ₑ’s from distant nuclear reactors. We find fewer v̅ₑ events than expected from standard assumptions about v̅ₑ propagation at the 99.95% C.L. In a 162 ton ∙ yr exposure the ratio of the observed inverse β-decay events to the expected number without v̅ₑ disappearance is 0.611 ± 0.085(stat) ± 0.041(syst) for v̅ₑ energies ˃ 3.4 MeV. In the context of two-flavor neutrino oscillations with CPT invariance, all solutions to the solar neutrino problem except for the “large mixing angle” region are excluded.