We search for new long-lived particles which decay to Z^0 bosons by
looking for Z^0 -> e^+e^- decays with displaced vertices.  We find no evidence
for parent particles of the Z^0 with long lifetimes in 90 pb^-1 of data from
the CDF experiment at Fermilab.  We set a cross section limit as a function of
the lifetime of the parent particles for both a generic Z^0 parent and a
fourth-generation, charge -1/3 quark that decays into Z^0b.