Linear chains of metallic nanoparticles that are sequentially rotated about the chain axis display interesting polarization-sensitive optical properties. Such twisted chains posses and extend properties of chiral gratings and general periodic gratings. They are characterized by high anisotropy and polarization sensitivity, and have subwavelength transverse dimensions. These structures are shown to support transverse modes with distinct propagation wavenumbers and radiation properties, including slow (bound) and fast (radiative) modes. They also have stop bands of different types, resulting from coupling between distinct transverse modes, as well as coupling with different higher-order diffraction modes.