We show that the combination of two achiral components - atomic or molecular target plus a circularly polarized photon - can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon K-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti-)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral, if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In both scenarios, the circularly polarized photon defines a plane with a sense of rotation and an additional axis is defined by the CO molecule or one electron. This is sufficient to establish an unambiguous coordinate frame of well-defined handedness. To produce a chirally structured electron angular distribution, such a coordinate frame is necessary, but not sufficient. We show that additional electron-electron interaction or scattering processes are needed to create the chiral angular distribution.
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