  One of the open questions of the strong interaction theory is the existence
of the Odderon, which is an unambiguous prediction of Quantum Chromodynamics,
but still not confirmed in the experiment. In this paper we propose the study
of the diffractive $\eta_c$ photoproduction in coherent interactions as a new
alternative to probe the Odderon in $pp$ and $PbPb$ collisions at CERN - LHC.
As the Pomeron exchange cannot contribute to this process, its observation
would indicate the existence of the Odderon. We predict total cross sections of
order of $pb \, (\mu b)$ for $pp \, (PbPb)$ collisions and large values for the
event rates/year, which makes, in principle, the experimental analysis of this
process feasible at LHC.
