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We present the results of a search for pair production of a fourth-generation charge -⅓ quark (b′) in √s =1.8 TeV pp collisions using 88 pb-1 of data obtained with the Collider Detector at Fermilab. We assume that both quarks decay via the flavor-changing neutral current process b′ → bZ0 and that the b′ mass is greater than mz+ mb. We studied the decay mode b′b̅′→ Z0Z0 bb̅ where one Z0 decays into e+e- or μ+μ-and the other decays hadronically, giving a signature of two leptons plus jets. An upper limit on the σ pp̅→b′b̅′x [B(b′→ bZ0)]2 is established as a function of the b0 mass. We exclude at 95% confidence level a b′ quark with mass between 100 and 199 GeV/c2 for B(b′→ bZ0)=100%.