  The top quark forward-backward asymmetry measured at the Tevatron collider
shows a large deviation from standard model expectations. Among possible
interpretations, a non-universal $Z^\prime$ model is of particular interest as
it naturally predicts a top quark in the forward region of large rapidity. To
reproduce the size of the asymmetry, the couplings of the $Z^\prime$ to
standard model quarks must be large, inevitably leading to copious production
of same-sign top quark pairs at the energies of the Large Hadron Collider
(LHC). We explore the discovery potential for $tt$ and $ttj$ production in
early LHC experiments at 7-8 TeV and conclude that if {\it no} $tt$ signal is
observed with 1 fb$^{-1}$ of integrated luminosity, then a non-universal
$Z^\prime$ alone cannot explain the Tevatron forward-backward asymmetry.
