  We explore the sensitivity of the LHC at 14 TeV centre-of-mass energy (LHC14)
to the single production and decay of top-antitop resonances in the four-top
final state. We focus on the same-sign dilepton channel, and work within a
simplified model with a vector boson coupling to the Standard Model only via
its interactions with right-handed top quarks. We find it is possible to
discover (exclude) such a vector boson with 300 fb$^{-1}$ of integrated
luminosity up to a mass of 1.2 (1.6) TeV for a modest coupling to tops of
$g_\rho$=2. We present our results as an exclusion limit on the
cross-section$\times$branching ratio for ease of recasting, and interpret them
in the context of the gauge-singlet vector boson $\rho_X$ present in many
simple Composite Higgs theories.
