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 30011D-1 of integrated luminosity up to a mass of 1.2 (1.6) TeV for a modest coupling to tops of gp = 2. We present our results as an exclusion limit on the cross-section x branching ratio for ease of recasting, and interpret them in the context of the gauge -singlet vector boson px present in many simple Composite Higgs theories.