  We consider the charmonium production in thermalized hadronic medium created
in ultrarelativistic heavy ion collisions at LHC energy.
  The calculations for the secondary $J/\psi$ and $\psi^,$ production by $D\bar
D$ annihilation are performed within a kinetic model taking into account the
space-time evolution of a longitudinally and transversely expanding medium. We
show that the secondary charmonium production appears almost entirely during
the mixed phase and it is very sensitive to the charmonium dissociation cross
section with co-moving hadrons. Within the most likely scenario for the
dissociation cross section of the $J/\psi$ mesons their regeneration in the
hadronic medium will be negligible. The secondary production of $\psi^,$ mesons
however, due to their large cross section above the threshold, can
substantially exceed the primary yield.
