  To investigate $Z'$ phenomenology model-independent, we combine chiral
effective theory with anomaly cancellation conditions without any other model
input. We focus on $Z'$ mixings with $\gamma-Z$ in both mass and kinetic parts
and calculate contributions to oblique $S,T,U$. The three sets of anomaly-free
fermion $U(1)'$ charges parameterize the $Z'$ interactions with fermions. The
cancellation of the $[U(1)']^3$ anomaly and mixing gravitational-gauge anomaly
determines the number of right-handed neutrinos. We also find a novel relation
between the charge assignments and Stueckelberg coupling in terms of the
renormalized electromagnetic current. A global fit to the electroweak precise
observables shows that typical values for the mixing parameters are of order
$10^{-3}$. In spite of this strict limit, we obtain a negative $S$ parameter
contribution.
