  We theoretically analyze spin filtering in two-terminal systems, induced by
the spin-orbit interaction (SOI), as a possible origin of the
``chirality-induced spin selectivity'' (CISS) effect observed experimentally in
chiral molecules, such as DNA. Due to Bardarson's theorem, spin filtering
cannot be realized in a molecule containing one orbital-channel. However, when
two orbitals are involved, SOI can induce spin filtering in a molecule coupled
to two terminals without braking time-reversal symmetry. In particular, we
provide an example of a $4 \times 4$ reflection matrix for a spinful electron
passing through a molecule containing two orbital-channels, which complies with
Bardarson's theorem and produces a finite spin conductance. As a microscopic
toy model realizing a single strand of DNA, we consider a $p$-orbital helical
atomic chain with intra-atomic SOI's and a strong crystalline field along the
helix. This model exhibits two-orbital spin filtering: For various parameters
preserving the helical symmetry, the model hosts spin asymmetric states
carrying pairs of up and down spins propagating in opposite directions. The
typical energy scale of the helical states is the product of the intra-atomic
SOI and the curvature. The large value of this energy identifies our model as a
likely candidate to explain the CISS in organic molecules.
