  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.
