In this seminar I would like to report on our recent work 2402.19134 where we suggest exclusive production of chi_c charmonia as a potential channel to detect the odderon at the EIC. Chi_c scalar, axial vector and tensor states with J = 0, 1, 2 are all C-even and so in e-p collisions the process is realized either through a photon or an odderon exchange in the t-channel with the proton. As the odderon and photon contributions add up coherently in the amplitude we pay special attention to their relative phase and find a constructive interference. This is so at the initial, moderate x, where a light-front quark model of the proton determines the odderon matrix element, but also after evolution to small-x for which the odderon amplitude is obtained from the Balitsky-Kovchegov equation for the dipole. We worked out the light-cone wave functions for all the J = 0, 1, 2 chi_c quarkonia and the overlaps with the photon wave functions allowing us to compute the gamma*p and the ep cross sections for the EIC kinematics. While the photon contribution alone dominates the low-t region, thanks to the Landshoff mechanism, the odderon contribution becomes important at |t| ~ 1 GeV^2. In the region of interest of about 0.5 GeV^2 |t| < 1.5 GeV^2 the total cross section exceeds the photon cross section alone by about a factor of 4. We conclude that the constructive intereference of the odderon and the photon along with a significant branching ratio of chi_c to J/psi + gamma leads to a prediction of about a dozen of chi_c's events per month at the highest ep collision energy at the EIC and thanks to its high luminosity. This suggests that data collection in a span of a couple of months to a year could be enough to discover the odderon at the EIC.
