The MiniBooNE experiment at Fermilab reports results from a search for $bar u_mu rightarrow bar u_e$ oscillations, using a data sample corresponding to $5.66 times 10^{20}$ protons on target. An excess of $20.9 pm 14.0$ events is observed in the energy range $475<E_ u^{QE}<1250$ MeV, which, when constrained by the observed $bar u_mu$ events, has a probability for consistency with the background-only hypothesis of 0.5%. On the other hand, fitting for $bar{ u}_{mu}rightarrowbar{ u}_e$ oscillations, the best-fit point has a $chi^2$-probability of 8.7%. The data are consistent with $bar u_mu rightarrow bar u_e$ oscillations in the 0.1 to 1.0 eV$^2$ $Delta m^2$ range and with the evidence for antineutrino oscillations from the Liquid Scintillator Neutrino Detector at Los Alamos National Laboratory.