The observation of the bottom, strange baryon {Xi}{sup 0}{sub b} through the decay chain {Xi}{sup 0}{sub b} {yields} {Xi}{sup +}{sub c} {pi}{sup -}, where {Xi}{sup +}{sub c} {yields} {Xi}{sup -} {pi}{sup +} {pi}{sup +}, {Xi}{sup -} {yields} {Lambda} {yields} p {pi}{sup -}, is reported using data corresponding to an integrated luminosity of 4.2 ft{sup -1} from p{anti p} collisions at {radical}{ovr s} = 1.96 TeV recorded with the Collider Detector at Fermilab. A signal of 25.3{sup +5.6}{sub -5.4} candidates is observed whose probability of arising from a background fluctuation is 3.6 x 10{sup -12}, corresponding to 6.8 Gaussian standard deviations. The {Xi}{sup 0}{sub b} mass is measured to be 5787.8 {+-} 5.0(stat) {+-} 1.3(syst) MeV/c{sup 2}. In addition, the {Xi}{sup -}{sub b} is observed through the process {Xi}{sup -}{sub b} {yields} {Xi}{sup 0}{sub c} {pi}{sup -}, where {Xi}{sup 0}{sub c} {yields} {Xi}{sup -} {pi}{sup +}, {Xi}{sup -} {yields} {Lambda} {pi}{sup -}, and {Lambda} {yields} p {pi}{sup -}.