We have searched for the baryon-containing radiative penguin decays B^- -> Lambda p-bar gamma and B^- -> Sigma^0 p-bar gamma, using a sample of 9.7 million BBbar events collected at the Upsilon(4S) with the CLEO detector. We find no evidence for either, and set 90% confidence level upper limits for photons with B rest frame energy greater than 2.0 GeV of [Br(B^- -> Lambda p-bar gamma) + 0.3 Br(B^- -> Sigma^0 p-bar gamma)] < 3.3 x 10^-6, [Br(B^- -> Sigma^0 p-bar gamma) + 0.4 Br(B^- -> Lambda p-bar gamma)] < 6.4 x 10^-6. From the latter, we estimate (for photons with B rest frame energy greater than 2.0 GeV) Br(B -> X_s gamma, X_s containing baryons) < 3.8 x 10^-5. This limit implies upper limits on corrections to CLEOs recent measurement of branching fraction, mean photon energy, and variance in photon energy from b -> s gamma that are less than half the combined statistical and systematic errors quoted on these quantities.
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