We report the results of x-ray-scattering studies of individual helical ribbons formed in multicomponent solutions of cholesterol solubilized by various surfactants. The solutions were chemically defined lipid concentrate (CDLC) and model bile. In these and many analogous multicomponent surfactant-cholesterol solutions, helical ribbons of two well defined pitch angles, namely 11 degrees and 54 degrees, are formed. We have suggested previously that this remarkable stability results from an underlying crystalline structure of the sterol ribbon strips. Using a synchrotron x-ray source, we have indeed observed Bragg reflections from individual ribbons having 11 degrees pitch angle. We have been able to deduce the parameters of the unit cell. The crystal structure of these ribbons is similar to that of cholesterol monohydrate, with the important difference that the length of the unit cell perpendicular to the cholesterol layers is tripled. We discuss possible origins for this triplication as well as the connection between the crystalline structure and the geometrical form of the helical ribbons.