In the formation of chiral crystals, the tendency for twist in the orientation of neighboring molecules is incompatible with ordering into a lattice: Twist is expelled from planar layers at the expense of local strain. We report the ordered state of a neat material in which a local chiral structure is expressed as twisted layers, a state made possible by spatial limitation of layering to a periodic array of nanoscale filaments. Although made of achiral molecules, the layers in these filaments are twisted and rigorously homochiral--a broken symmetry. The precise structural definition achieved in filament self-assembly enables collective organization into arrays in which an additional broken symmetry--the appearance of macroscopic coherence of the filament twist--produces a liquid crystal phase of helically precessing layers.