We propose a hypothetical heavy leptonium, the scalar bound state of an exotic lepton-antilepton pair, as a candidate for the recent 750 GeV resonance in the early LHC Run 2 data. Such a para-leptonium is dominantly produced via photon-photon fusion at the LHC and decays into a photon pair with a significant branching fraction. In addition, our model predicts a companion spin-1 ortho-leptonium bound state, which can decay to $W^+W^-$, $fbar{f}$ and three photons. Under the LHC and the electroweak precision observables bounds, we find that the observed excess of 750 GeV diphoton events can be explained within $2sigma$ accuracy for $Y_{L} approx 4.8 - 7.2$ for the minimal case in our scenario. The observation of the ortho-leptonium in the dilepton channel will be the smoking gun for our scenario.
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