A chiral scattering molecule has the ability to interact differently with circularly polarized light of opposite polarization. This phenomenon has been termed circular intensity differential scattering. It is shown that the differential-scattering phenomenon contributes to the total optical rotatory dispersion (ORD) of the sample. This contribution is independent of the presence of chromophores in the sample. From two general relations, (1) the Kronig–Kramers transforms, obeyed by linear, causal systems, and (2) the optical theorem, a result of energy conservation and power flow, the contribution of the preferential scattering of circularly polarized light to the ORD of the sample is formally obtained. It is seen that this contribution takes place through the circular preferential removal of the coherent part of the wave, i.e., the extinction (by means of scattering) of the transmitted radiation. It is shown that the use of approximations in the description of the internal field in the scattering equations can equivocally predict the absence of a scattering-dependent ORD contribution. © 1984 Optical Society of America.