A search for contributions to the reaction ep --> epi(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(gammap --> 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 < < 0.3 GeV2. 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. (C) 2002 Elsevier Science B.V. All rights reserved.