A model of a light Z' boson is constructed and phenomenological bounds
are derived. This Z' boson arises from a very simple extension to the
standard model, and it is constrained to be light because the vacuum
expectation values which generate its mass also break the electroweak
gauge group. It is difficult to detect experimentally because it coupl
es exclusively or primarily (depending on symmetry-breaking details) t
o second and third generation leptons. However, if the Z' boson is suf
ficiently light, then there exists the possibility of the two-body dec
ay tau --> muZ' occurring. This will provide a striking signature to t
est the model.