The MiniBooNE experiment at Fermilab reports results from a search for ¯ν_{μ}→¯ν_{e} oscillations, using a data sample corresponding to 5.66×10²⁰ protons on target. An excess of 20.9±14.0 events is observed in the energy range 475<E_{ν}^{QE}<1250 MeV, which, when constrained by the observed ¯ν_{μ} events, has a probability for consistency with the background-only hypothesis of 0.5%. On the other hand, fitting for ¯ν_{μ}→¯ν_{e} oscillations, the best-fit point has a χ² probability of 8.7%. The data are consistent with ¯ν_{μ}→¯ν_{e} oscillations in the 0.1 to 1.0 eV² Δm² range and with the evidence for antineutrino oscillations from the Liquid Scintillator Neutrino Detector at Los Alamos National Laboratory.