  We compute the cross section for exclusive production of a photon associated
with a heavy quarkonium H of charge-conjugation parity C=+1 from e+ e-
annihilation into a virtual photon at the center-of-momentum energy
root-s=10.58 GeV. The NRQCD factorization formulas for the differential and
total cross sections are obtained at leading order in the strong coupling and
in the relative velocity of the heavy quark in the quarkonium rest frame. The
predicted cross sections for the S-wave spin-singlet cases are about 80 fb and
50 fb for H = eta_c and eta_c(2S), respectively. Among P-wave spin-triplet
charmonia, chi_{c1} has a particularly large cross section of about 14 fb. The
cross sections for bottomonium states eta_b and chi_{bJ} are about 3 fb. A
rough estimate of the background reveals that the signal significances for
charmonium processes are sufficiently large enough to be detected with ease
with the integrated luminosities available at the present B factories.
