Chirality-induced spin selectivity has been reported in many experiments, but a generally accepted theoretical explanation has not yet been proposed. Here, we introduce a simple model system of a straight cylindrical free-electron wire containing a helical string of atomic scattering centers with spin-orbit interaction. The advantage of this simple model is that it allows deriving analytical expressions for the spin scattering rates, such that the origin of the effect can be easily followed. We find that spin-selective scattering can be viewed as resulting from the constructive interference of partial waves scattered by the spin-orbit terms. We demonstrate that forward scattering rates are independent of spin, while back scattering is spin dependent over wide windows of energy. Although the model does not represent the full details of electron transmission through chiral molecules, it clearly reveals a mechanism that could operate in chiral systems.