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 $tbar{t}Z^prime$ 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.
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