  We explore the physics of a new neutral gauge boson, ($Z^\prime$), coupling
to only third-generation particles with a mass near the electroweak gauge boson
mass poles. A $Z^\prime$ boson produced by top quarks and decaying to tau
leptons is considered. With a simple search strategy inspired by existing
analyses of the standard model gauge boson production in association with top
quarks, we show that the Large Hadron Collider has good exclusionary power over
the model parameter space of the $Z^\prime$ boson even at the advent of the
high-luminosity era. It is shown that the $t\bar{t}Z^\prime$ process allows one
to place limits on right-handed top couplings with a $Z^\prime$ boson that
preferentially couples to third generation fermions, which are at present very
weakly constrained.
