  Theory and phenomenology of the eta_c photo- and electroproduction is
developed from the point of view of probing the odderon singularity in QCD
which corresponds to the three gluon exchange mechanism. This mechanism leads
to the cross-sections which are independent of W^2 for the exchange of three
non-interacting gluons or exhibit increase with increasing W^2 (or 1/x) for the
odderon intercept above unity. The \eta_c electroproduction in the three gluon
exchange mechanism is shown to be entirely controlled by the transversely
polarised virtual photons. The magnitude of the eta_c photoproduction
cross-section is estimated to be around 11-45pb. The t-dependence of the
differential cross-section is also discussed.
