  The MiniBooNE experiment at Fermilab reports results from a search for $\bar
\nu_\mu \rightarrow \bar \nu_e$ 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 $475<E_\nu^{QE}<1250$ MeV, which, when
constrained by the observed $\bar \nu_\mu$ events, has a probability for
consistency with the background-only hypothesis of 0.5\%. On the other hand,
fitting for $\bar{\nu}_{\mu}\rightarrow\bar{\nu}_e$ oscillations, the best-fit
point has a $\chi^2$-probability of 8.7\%. The data are consistent with $\bar
\nu_\mu \rightarrow \bar \nu_e$ 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.
