  We report the first direct observation of the strange b baryon Xi_b^{-}. We
reconstruct the decay Xi_b^{-} to J/psi Xi^{-}, with J/psi to dimuons and
Xi^{-} to Lambda pion, in ppbar collisions at sqrt(s) = 1.96 TeV. Using 1.3
fb^{-1} of data collected by the D0 detector, we observe 15.2 +/- 4.4(stat.)+
1.9/-0.4(syst.) Xi_b^{-} candidates at a mass of 5.774 +/- 0.011(stat.) +/-
0.015 (syst.) GeV. The significance of the observed signal is 5.5 sigmas,
equivalent to a probability of 3.3 X 10^{-8} of it arising from a background
fluctuation. Normalizing to the decay Lambda_b to J/psi Lambda, we measure the
relative rate to be 0.28 +/- 0.09(stat.)+ 0.09/-0.08 (syst.).
