  We calculate the exclusive cross sections for e^+ e^- annihilation into two
charmonium states through a virtual photon. Purely electromagnetic
contributions are surprisingly large, changing the cross sections by as much as
21%. The predicted cross section for J/psi + eta_c is about an order of
magnitude smaller than a recent measurement by the BELLE Collaboration,
although part of the discrepancy can be attributed to large relativistic
corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and
S-wave + D-wave charmonium states are also calculated. It may be possible to
discover the D-wave state eta_{c2}(1D) at the B factories through the mode
J/psi+\eta_{c2}, whose cross section is predicted to be about a factor of 10
smaller than J/psi + eta_c.
