  Time-reversal symmetric charge and spin transport through a molecule
comprising two-orbital channels and connected to two leads is analyzed. It is
demonstrated that spin-resolved currents are generated when spin-flip processes
are accompanied by a flip of the orbital channels. This surprising finding does
not contradict Bardarson's theorem [J. H. Bardarson, J. Phys. A: Math. Theor.
41, 405203 (2008)] for two-terminal junctions: the transmission does possess
two pairs of doubly-degenerate eigenvalues as required by the theorem. The
spin-filtering effect is explicitly demonstrated for a two-terminal chiral
molecular junction, modeled by a two-orbital tight-binding chain with
intra-atomic spin-orbit interactions (SOI). In the context of transport through
organic molecules like DNA, this effect is termed "chirality-induced spin
selectivity" (CISS). The model exhibits spin-splitting without breaking
time-reversal symmetry: the intra-atomic SOI induces concomitant spin and
orbital flips. Examining these transitions from the point of view of the Bloch
states in an infinite molecule, it is shown that they cause shifts in the Bloch
wave numbers, of the size of the reciprocal single turn, whose directions
depend on the left-and right-handedness of the helix. As a result, spin-up and
spin-down states propagate in the opposite directions, leading to the CISS
effect. To further substantiate our picture, we present an
analytically-tractable expression for the 8$\times$8 scattering matrix of such
a (single) molecule.
