  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
color-singlet spin-0 toponium $\eta_t$ bound state of a top and anti-top quark,
that then decays di-leptonically ($gg\to\eta_t \to \bar\ell \ell b \bar{b} \nu
\bar{\nu}$). We find strong correlations favoring 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.
