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We study reported deviations between observations and theoretical predictions associated with the production of a pair of di-leptonically decaying top quarks at the LHC, and we examine the possibility that they reflect a signal of toponium formation. We investigate the production by gluon fusion of a colour-singlet spin-0 toponium bound state of a top and anti-top quark, that then decays di-leptonically. We find strong correlations favouring the production of di-lepton systems featuring a small angular separation in azimuth and a small invariant mass. Although toponium production only contributes to 0.8% of the total top-quark pair-production cross section at the 13 TeV LHC, there is a possibility that it can account for observed excesses in the narrow edges of phase space. We propose a method to discover toponium formation by `reconstructing' both its top and anti-top quark constituents in the di-lepton channel.