We report evidence for a narrow structure, X(5568), in the decay sequence X(5568)→B_{s}^{0}π^{±}, B_{s}^{0}→J/ψϕ, J/ψ→μ^{+}μ^{-}, ϕ→K^{+}K^{-}. This is evidence for the first instance of a hadronic state with valence quarks of four different flavors. The mass and natural width of this state are measured to be m=5567.8±2.9(stat)_{-1.9}^{+0.9}(syst) MeV/c^{2} and Γ=21.9±6.4(stat)_{-2.5}^{+5.0}(syst) MeV/c^{2}. If the decay is X(5568)→B_{s}^{*}π^{±}→B_{s}^{0}γπ^{±} with an unseen γ, m(X(5568)) will be shifted up by m(B_{s}^{*})-m(B_{s}^{0})∼49 MeV/c^{2}. This measurement is based on 10.4 fb^{-1} of pp[over ¯] collision data at sqrt[s]=1.96 TeV collected by the D0 experiment at the Fermilab Tevatron collider.