  Theoretical and phenomenological predictions of $\mathcal{BR}(K_L\rightarrow
(\mu^+\mu^-) \gamma)\sim7\times10^{-13}$ are presented for different model form
factors $F_{K_L\gamma\gamma^*}(Q^2)$. These rates are comparable to existing
and near-term rare $K_L$ decay searches at J-PARC and CERN, indicating a
discovery of true muonium is possible. The model uncertainties are sufficiently
small that detection of true muonium could discriminate between the form factor
models. Further discussion of potential backgrounds is made.
