  Leptophobic Z' gauge bosons can appear in models with an E_6 gauge symmetry.
We show that flavour-changing neutral currents can be generated in some of
these models due to the mixing of the ordinary d_R, s_R and b_R quark fields
with the exotic h_R. Because the Z' does not couple to charged leptons, the
constraints on the flavour-changing couplings U^{Z'}_{db} and U^{Z'}_{sb} are
relatively weak. Indeed, B_q--Bbar_q mixing (q=d,s) can be dominated by Z'
exchange, which will affect CP-violating rate asymmetries in B decays. Rare
hadronic B decays can also be affected, while decays involving charged leptons
will be unchanged.
