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We report the first observation of diffractive J/ψ(→μ+μ-) production in p̅p collisions at √s= 1.8 TeV. Diffractive events are identified by their rapidity gap signature. In a sample of events with two muons of transverse momentum pT,/sub> μ> 2 GeV/c within the pseudorapidity region |η| <1.0, the ratio of diffractive to total J/ψ production rates is found to be RJ/ψ=[1.45 ± 0.25]%. The ratio RJ/ψ(x) is presented as a function of x-Bjorken. By combining it with our previously measured corresponding ratio Rjj(x) for diffractive dijet production, we extract a value of 0.59 ± 0.15 for the gluon fraction of the diffractive structure function of the proton.