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