We have searched for heavy neutral gauge bosons (Z') in dielectron
and dimuon decay modes using 110 pb^-1 of pbar p collisions at sqrt s = 1.8
TeV collected with the Collider Detector at Fermilab.  We present a limit on
the production cross section times branching ratio of a Z' boson decaying into
dileptons as a function of Z' mass.  For mass M_Z' > 600 GeV/c^2, the upper
limit is 40 fb at 95% confidence level.  We set lower mass limits of 690, 590,
620, 595, 565, 630 and 600 GeV/c^2 for Z'_SM, Z_psi, Z_eta, Z_chi, Z_I, Z_LR,
and Z_ALRM, respectively.