We estimate the production of two meson pairs in high energy photon photon collisions produced in ultraperipheral collisions at LHC. We show that the study of charge asymmetries may reveal the existence of the perturbative Odderon and discuss the concrete event rates expected at the LHC. Sizable rates and asymmetries are expected in the case of proton-proton collisions and medium values of gamma-gamma energies sqrt{s_{gamma gamma}} approx 20GeV. Proton-proton collisions will benefit from a high rate due to a large effective gamma-gamma luminosity and ion-ion collisions with a somewhat lower rate from the possibility to trigger on ultraperipheral collisions and a reduced background from strong interactions.
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