Bottom baryons decaying to a J/psi meson and a hyperon are reconstructed using 1.0 fb^{-1} of data collected in 2011 with the LHCb detector. Significant Lambda_b^0 rightarrow J/psi Lambda, Xi_b^-rightarrow J/psi Xi^- and Omega_b^- rightarrow J/psi Omega^- signals are observed and the corresponding masses are measured to be M(Lambda_b^0) = 5619.53 pm 0.13 (stat) pm 0.45 (syst) MeV/c^2, M(Xi_b^-) = 5795.8 pm 0.9 (stat) pm 0.4 (syst) MeV/c^2, M(Omega_b^-) = 6046.0 pm 2.2 (stat) pm 0.5 (syst) MeV/c^2, while the differences with respect to the Lambda_b^0 mass are M(Xi_b^-)-M(Lambda_b^0) = 176.2 pm 0.9 (stat) pm 0.1 (syst) MeV/c^2, M(Omega_b^-)-M(Lambda_b^0) = 426.4 pm 2.2 (stat) pm 0.4 (syst) MeV/c^2. These are the most precise mass measurements of the Lambda_b^0, Xi_b^- and Omega_b^- baryons to date. Averaging the above Lambda_b^0 mass measurement with that published by LHCb using 35 pb^{-1} of data collected in 2010 yields M(Lambda_b^0) = 5619.44 pm 0.13 (stat) pm 0.38 (syst) MeV/c^2.
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