The polarization properties of light absorption by molecular chromophores partially aligned by photoselection are presented in complete form. Circular dichroism (CD) in a photoselectively oriented ensemble of absorbers arises from two types of magnetic dipole terms and, in systems of low symmetry, from electric quadrupole terms, the relative contributions of these depending on the polarization properties of the probe and actinic light beams. The anisotropic circular dichroism measured in such experiments may contain information about molecular moments that is not directly available from other spectroscopic techniques, although separation of the magnetic dipole and electric quadruple contributions will be generally possible only in systems of C-2 or D-2 symmetry. Theoretical descriptions are presented of possible experimental configurations for measuring oriented CD by modulating circular polarization in the probe beam, exciting beam, or in dual beams, The possible effect of photoselection-orientation on the time evolution of circular dichroism signals measured in laser flash-photolysis experiments in discussed.