We report the observation of the bottom, doubly-strange baryon Ω−b through the decay chain Ω−b→J/ψΩ−, where J/ψ→μ+μ−, Ω−→ΛK−, and Λ→pπ−, using 4.2  fb−1 of data from pp¯ collisions at s√=1.96  TeV, and recorded with the Collider Detector at Fermilab. A signal is observed whose probability of arising from a background fluctuation is 4.0×10−8, or 5.5 Gaussian standard deviations. The Ω−b mass is measured to be 6054.4±6.8(stat)±0.9(syst)  MeV/c2. The lifetime of the Ω−b baryon is measured to be 1.13+0.53−0.40(stat)±0.02(syst)  ps. In addition, for the Ξ−b baryon we measure a mass of 5790.9±2.6(stat)±0.8(syst)  MeV/c2 and a lifetime of 1.56+0.27−0.25(stat)±0.02(syst)  ps. Under the assumption that the Ξ−b and Ω−b are produced with similar kinematic distributions to the Λ0b baryon, we find σ(Ξ−b)B(Ξ−b→J/ψΞ−)σ(Λ0b)B(Λ0b→J/ψΛ)=0.167+0.037−0.025(stat)±0.012(syst) and σ(Ω−b)B(Ω−b→J/ψΩ−)σ(Λ0b)B(Λ0b→J/ψΛ)=0.045+0.017−0.012(stat)±0.004(syst) for baryons produced with transverse momentum in the range of 6–20  GeV/c.