  We discuss the orientation of e+e- -> q qbar g events in terms of the polar
and azimuthal angles of the event plane w.r.t. the electron beam direction. We
define an asymmetry of the azimuthal-angle distribution, which, along with the
left-right forward-backward polar-angle asymmetry, is sensitive to
parity-violating effects in three-jet events; these have yet to be explored
experimentally. We have evaluated these observables at O(alpha_s) in
perturbative QCD and present their dependence on longitudinal beam polarisation
and c.m. energy. We also define a moments analysis in terms of the orientation
angles that allows a new and more detailed test of QCD by isolating the six
independent helicity cross-sections.
