We report the observation of the bottom, doubly-strange baryon Ωb− through the decay chain Ωb−→J/ψΩ−, where J/ψ→μ+μ−, Ω−→ΛK−, and Λ→pπ−, using 4.2 fb−1 of data from ppˉ 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 Ωb− mass is measured to be 6054.4±6.8(stat.)±0.9(syst.) MeV/c2. The lifetime of the Ωb− baryon is measured to be 1.13−0.40+0.53(stat.)±0.02(syst.) ps. In addition, for the Ξb− baryon we measure a mass of 5790.9±2.6(stat.)±0.8(syst.) MeV/c2 and a lifetime of 1.56−0.25+0.27(stat.)±0.02(syst.) ps. %These measurements were performed using 4.2 fb−1 of %data from ppˉ collisions at s=1.96 TeV, and %recorded with the Collider Detector at Fermilab. Under the assumption that the Ξb− and Ωb− are produced with similar kinematic distributions to the Λb0 baryon, we find σ(Λb0)B(Λb0→J/ψΛ)σ(Ξb−)B(Ξb−→J/ψΞ−)=0.167−0.025+0.037(stat.)±0.012(syst.) and σ(Λb0)B(Λb0→J/ψΛ)σ(Ωb−)B(Ωb−→J/ψΩ−)=0.045−0.012+0.017(stat.)±0.004(syst.) for baryons produced with transverse momentum in the range of 6−20 GeV/c.