In many skeletal support systems of plants and animals, cellulose, chitin, and collagen occur in the form of microfibrils ordered in a chiral nematic fashion (helicoids). However, these structures remain poorly understood due to the many constituents present in biological tissues. Here we report an in vitro system that attracts by its simplicity. Only one chemical component, cellulose, is present in the form of fibrillar fragments dispersed in water. Above a critical concentration the colloidal dispersion separates spontaneously into a chiral nematic liquid crystalline phase. On drying this phase solidifies into regularly twisted fibrillar layers that mimic the structural organization of helicoids in nature.