  Recently we have proved the factorization of NRQCD S-wave heavy quarkonium
production at all orders in coupling constant. In this paper we extend this to
prove the factorization of infrared divergences in $\chi_{cJ}$ production from
color singlet $c{\bar c}$ pair in non-equilibrium QCD at RHIC and LHC at all
orders in coupling constant. This can be relevant to study the quark-gluon
plasma at RHIC and LHC.
