We present the results of a search for pair production of a fourth-generation charge -1 / 3 quark (b(')) in sqrt[s] = 1.8 TeV p&pmacr; 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(')-->bZ(0) and that the b(') mass is greater than m(Z)+m(b). We studied the decay mode b(')b(');-->Z(0)Z(0)b&bmacr; where one Z0 decays into e(+)e(-) or &mgr;(+)&mgr;(-) and the other decays hadronically, giving a signature of two leptons plus jets. An upper limit on the sigma(p&pmacr;-->b(')b(');)x[B(b(')-->bZ(0))](2) is established as a function of the b(') mass. We exclude at 95% confidence level a b(') quark with mass between 100 and 199 GeV/c(2) for B(b(')-->bZ(0)) = 100%.