  Pion exchange in S-wave between hadrons that are themselves in a relative
S-wave is shown to shift energies by hundreds of MeV, leading to deeply bound
quasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopy
arises 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 and
charge-conjugation combinations, and comment on flavor exotic doubly charmed
states and bottomonium analogs. A search in $D\bar{D}3\pi$ is recommended to
test this hypothesis. An exotic $1^{-+}$ is predicted to occur in the vicinity
of the $Y$(4260).
