•We calculate the light-scattering spiral particles.•The magnitude of the circular-polarization signal can be greater than 10%.•A circular polarization opposition effect is observed for the first time. We calculate the light-scattering Mueller matrix elements of left-handed and right-handed spiral particles that have morphological chirality. For such orientation-averaged systems, none of the Mueller matrix elements are equal to zero, although basic relations do exist between enantiomers. The magnitude of the circular-polarization signal can be greater than 10%; however, in the backscattering region it can be significantly greater due to a manifestation of the coherent-backscattering mechanism. The magnitude of this circular-polarization opposition effect decreases with particle absorption and its width decreases with decreasing wavelength, which is consistent with the linear-polarization opposition effect and the intensity opposition effect.