  We present our results on charmonium production at the Large Hadron Collider
energies within the comover interaction model. The formalism includes both
comover dissociation of $J/\psi$'s and possible secondary $J/\psi$ production
through recombination. The estimation of this effect is made without involving
free parameters. The comover interaction model also incorporates an analytic
treatment of initial-state nuclear shadowing. With these tools, the model
successfully describes the centrality, transverse momentum and rapidity
dependence of the experimental data from PbPb collisions at the LHC energy of
$\sqrt{s} = 2.76$ TeV. We present predictions for PbPb collisions at $\sqrt{s}
= 5.5$ TeV.
