  We propose to look for the Odderon through the production of two pion pairs
in photon collisions at high energies. We calculate the corresponding matrix
elements in kT-factorization and discuss the possibility to reveal the
existence of the perturbative Odderon by charge asymmetries, relying on models
for the generalized distribution amplitudes of pi+ pi-. The application of this
strategy to ultraperipheral collisions at the LHC suffers from the difficulty
to trigger on interesting events and is plagued with severe background problems
in p-p mode. Electron - positron colliders like ILC seem to better suit this
physics.
