We present the results of a search for extraterrestrial electron antineutrinos (v̅ₑ) in the energy range 8.3MeV < E v̅ₑ < 31.8MeV using the KamLAND detector. In an exposure of 4.53 kton-year, we identify 25 candidate events. All of the candidate events can be attributed to background, most importantly neutral current atmospheric neutrino interactions, setting an upper limit on the probability of ⁸B solar vₑ's converting into v̅ₑ's at 5.3 x 10⁻⁵ (90% CL), if we assume an undistorted v̅ₑ shape. This limit corresponds to a solar v̅ₑ flux of 93 cm⁻²s⁻¹ or an event rate of 1.6 events (kton – year)⁻¹ above the energy threshold (E v̅ₑ ≥ 8.3MeV). The present data also allows us to set more stringent limits on the diffuse supernova neutrino flux and on the annihilation rates for light dark matter particles.