The associated production of J/psi+ gamma at the CERN LHC is studied within
the NRQCD framework. The signal we focus on is the production of a J/psi a
nd an isolated photon produced back to back, with their transverse moments
balanced. It is shown that even for very large values of transverse momentu
m (pr similar to 50 GeV) the dominant contribution to this process is nor f
ragmentation. This is because of the fact that fragmentation-type contribut
ions to the cross section come from only a <q(q)over bar> initial state, wh
ich is suppressed at the LHC. We identify gg-initiated diagrams higher-orde
r in a, which do have fragmentation-type vertices. We find, however, that t
he contribution of these diagrams is negligibly small. [S0556-2821(99)03613
-9].