  A search for contributions to the reaction ep-> e pi^0 N^* from
photon-Odderon fusion in the photoproduction regime at HERA is reported, at an
average photon-proton centre-of-mass energy <W> = 215 GeV. The measurement
proceeds via detection of the pi^0 decay photons, a leading neutron from the
N^* decay, and the scattered electron. No pi^0 signal is observed and an upper
limit on the cross section for the photon-Odderon fusion process of sigma(gamma
p -> pi^0 N^*) < 49 nb at the 95% confidence level is derived, integrated over
the experimentally accessible range of the squared four-momentum transfer at
the nucleon vertex 0.02 < |t| < 0.3 Gev^2. This excludes a recent prediction
from a calculation based on a non-perturbative QCD model of a photon-Odderon
fusion cross section above 200 nb.
