  We calculate the cross section for the exclusive production of J^{PC}=0^{++}
glueballs G_0 in association with the J/psi in e^+e^- annihilation using the
pQCD factorization formalism. The required long-distance matrix element for the
glueball is bounded by CUSB data from a search for resonances in radiative
Upsilon decay. The cross section for e^+e^- -> J/psi+ G_0 at sqrt{s}=10.6 GeV
is similar to exclusive charmonium-pair production e^+e^- -> J/psi+h for
h=eta_c and chi_{c0}, and is larger by a factor 2 than that for h=eta_{c}(2S).
As the subprocesses gamma^* -> (c c-bar) (c c-bar) and gamma^* -> (c c-bar) (g
g) are of the same nominal order in perturbative QCD, it is possible that some
portion of the anomalously large signal observed by Belle in e^+ e^- -> J/psi X
may actually be due to the production of charmonium-glueball J/psi G_J pairs.
