  It is commonly accepted that the magnitude of a photoelectron circular
dichroism (PECD) is governed by the ability of an outgoing photoelectron wave
packet to probe the chiral asymmetry of a molecule. To be able to accumulate
this characteristic asymmetry while escaping the chiral ion, photoelectrons
need to have relatively small kinetic energies of up to a few tens of electron
volts. Here, we demonstrate a substantial PECD for very fast photoelectrons
above 500 eV kinetic energy released from methyloxirane by a participator
resonant Auger decay of its lowermost O $1s$-excitation. This effect emerges as
a result of the Fano interference between the direct and resonant
photoionization pathways, notwithstanding that their individual effects are
negligibly small. The resulting dichroic parameter has an anomalous dispersion,
i.e. it changes its sign across the resonance, which can be considered as an
analogue of the Cotton effect in the X-ray regime.
