  Charmonium production from the hadron gas formed in ultra-relativistic
heavy-ion collisions is studied. Using the $J/\psi$-hadron absorption cross
section determined from the nonperturbative quark-exchange model, which has a
peak value similar to that used in the comover model for $J/\psi$ suppression
and a thermally averaged value consistent from that extracted from $J/\psi$
data in heavy-ion collisions, we find that $J/\psi$ production from the hadron
gas is negligible in heavy-ion collisions at RHIC energies but is important at
LHC energies as a result of the large number of charm mesons produced at higher
energy collisions. The number of $J/\psi$ produced from these secondary
collisions at LHC may be comparable to that of primary $J/\psi$'s, which are
expected to be dissociated in the quark-gluon plasma created in the collisions,
leading thus to a possible absence of $J/\psi$ suppression. Similar results are
obtained for $\psi^\prime$ production in ultra-relativistic heavy-ion
collisions.
