We consider the charmonium production in the thermalized hadronic medium cr
eated in ultrarelativistic heavy ion collisions at LHC energy. The calculat
ions for secondary J/psi and psi' production by D (D) over bar annihilation
are performed within a kinetic model taking into account the space-time ev
olution of a longitudinally and transversely expanding medium. We show that
secondary charmonium production appears almost entirely during the mixed p
hase, and that it is very sensitive to the charmonium dissociation cross se
ction with co-moving hadrons. Within the most likely scenario for the disso
ciation cross section of the J/psi mesons their regeneration in the hadroni
c medium will be negligible. The secondary production of psi' mesons howeve
r, due to their large cross section above the threshold, can substantially
exceed the primary yield.