We report the first direct observation of the strange b baryon Xi(b)- (Xi(b)+). We reconstruct the decay Xi(b)- -->J/psiXi-, with J/psi-->mu+mu-, and Xi--->Lambdapi--->ppi-pi- in pp collisions at square root of s =1.96 TeV. Using 1.3 fb(-1) of data collected by the D0 detector, we observe 15.2 +/- 4.4(stat)(-0.4)(+1.9)(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 sigma, equivalent to a probability of 3.3 x 10(-8) of it arising from a background fluctuation. Normalizing to the decay Lambda(b)-->J/psiLambda, we measure the relative rate sigma(Xi(b-) x B(Xi)b})- -->J/psiXi-)/sigma(Lambda(b)) x B(Lambda(b)-->J/psiLambda) = 0.28+/-0.09(stat)(-0.08)(+0.09)(syst).