Bottom baryons decaying to a J/ψ meson and a hyperon are reconstructed using 1.0 fb(-1) of data collected in 2011 with the LHCb detector. Significant Λ(b)(0) → J/ψΛ, Ξ(b((-) → J/ψΞ(-) and Ω(b)(-) → J/ψΩ(-) signals are observed and the corresponding masses are measured to be M(Λ(b)(0))=5619.53 ± 0.13(stat.) ± 0.45(syst.) MeV/c(2), M(Ξ(b)(-)) = 5795.8 ± 0.9(stat.) ± 0.4(syst.) MeV/c(2), M(Ω(b)(-)) = 6046.0 ± 2.2(stat.) ± 0.5(syst.) MeV/c(2) , while the differences with respect to the Λ(b)(0) mass are M(Ξ(b)(-))-M(Λ(b)(0))=176.2 ± 0.9(stat.) ± 0.1(syst.) MeV/c(2), M(Ω(b)(-))-M(Λ(b)(0))=426.4 ± 2.2(stat.) ± 0.4(syst.) MeV/c(2). These are the most precise mass measurements of the Λ(b)(0), Ξ(b)(-) and Ω(b)(-) baryons to date. Averaging the above Λ(b)(0) mass measurement with that published by LHCb using 35 pb(-1) of data collected in 2010 yields M(Λ(b)(0)) = 5619.44 ± 0.13(stat.)± 0.38(syst.) MeV/c(2).