We study reported deviations between observations and theoretical predictions associated with the production of a pair of dileptonically 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 color-singlet spin-0 toponium ${\eta }_t$ bound state of a top and antitop quark, that then decays dileptonically ($gg\to {\eta }_t\to \overline{\ell }\ell b\overline{b}\nu \overline{\nu }$). We find strong correlations favoring the production of dilepton 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 antitop quark constituents in the dilepton channel.