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Pion exchange in S-wave between hadrons that are themselves in a relativeS-wave is shown to shift energies by hundreds of MeV, leading to deeply boundquasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopyarises consistent with enigmatic charmonium states observed above 4 GeV in$e^+e^-$ annihilation. A possible explanation of $Y(4260)\to \psi\pi\pi$ and$Y(4360) \to \psi'\pi\pi$ is found. We give results for all isospin andcharge-conjugation combinations, and comment on flavor exotic doubly charmedstates and bottomonium analogs. A search in $D\bar{D}3\pi$ is recommended totest this hypothesis. An exotic $1^{-+}$ is predicted to occur in the vicinityof the $Y$(4260).

Novel Charmonium and Bottomonium Spectroscopies due to Deeply Bound Hadronic Molecules from Single Pion Exchange