  An extra $U(1)'$ model with $Z'$ coupled only to the right-handed (RH)
up-type quarks has been one of the popular models for the Tevatron top
forward-backward asymmetry (FBA), and has been excluded by the same-sign
top-pair productions at the LHC. However, the original $Z'$ model is not
physical, since the up-type quarks are massless including the top quark. This
disaster can be evaded if the Higgs sector is extended by including new Higgs
doublets with nonzero $U(1)'$ charges. We find that some parameter regions
could achieve not only the top FBA at the Tevatron, but also the charge
asymmetry at the LHC without exceeding the upper limit of the same-sign
top-quark pair production at the LHC. The lesson is that it is mandatory to
extend the Higgs sector whenever one considers chiral gauge symmetries beyond
the SM gauge group. Otherwise some fermions remain massless, and thus it is
meaningless to work on phenomenology without the extra Higgs doublets with new
chiral gauge charges.
