We report the observation of the doubly strange b baryon Omega(-)(b) in the decay channel Omega(-)(b) -> J/psi Omega(-), with J/psi -> mu(+)mu(-) and Omega(-) -> Lambda K- -> (p pi(-))K-, in p (p) over bar collisions at root s = 1.96 TeV. Using approximately 1.3 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron Collider, we observe 17.8 +/- 4.9(stat) +/- 0.8(syst) Omega(-)(b) signal events at a mass of 6.165 +/- 0.010(stat) +/- 0.013(syst) GeV. The significance of the observed signal is 5.4 sigma, corresponding to a probability of 6.7 x 10(-8) of it arising from a background fluctuation.