  The Large Hadron Collider (LHC) is sensitive to new heavy gauge bosons that
produce narrow peaks in the dilepton invariant mass spectrum up to about
$m_{Z'}\sim 5$ TeV. $Z'$s that are too heavy to produce directly can reveal
their presence through interference with Standard Model dilepton production. We
show that the LHC can significantly extend the mass reach for such $Z'$s by
performing precision measurements of the shape of the dilepton invariant mass
spectrum. The high luminosity LHC can exclude, with 95$\%$ confidence, new
gauge bosons as heavy as $m_{Z'} \sim 10-20$ TeV that couple with gauge
coupling strength of $g_{Z'} \sim 1-2$.
