We present the results of a search for new particles with long
lifetime that decay to a Z0 boson. A long-lived parent of the Z0 is
predicted by several models in addition to being an experimentally clean
channel. We vertex dimuons with invariant mass near the Z0 peak and study
the decay length distribution. No evidence of a long-lived component is
found, and cross-section limits are presented using the fourth generation
quark model.