The organization of nanocolloidal liquid crystals in constrained geometries has fundamental and practical importance, since under confinement, liquid crystals contain stable topological defects that can serve as templates for nanoparticle organization. Three-dimensional confinement of cholesteric (Ch) liquid crystals formed by cellulose nanocrystals (CNCs) have been extensively studied; however, their two-dimensional confinement remains under-investigated. Here, we report the results of systematic experimental studies of two-dimensional confinement of Ch-CNC liquid crystal in cylindrical capillaries with varying inner diameters. Confinement resulted in phase separation of the Ch-CNC liquid crystal into a Ch shell formed by concentric CNC pseudolayers with the helicoidal axis perpendicular to the inner surface of the capillary walls, and a micrometer-diameter isotropic core thread running parallel to the long axis of the capillary. The morphology of the confined Ch-CNC liquid crystal varied when progressively increasing the degree confinement. Finally, we show that phase separation of the Ch-CNC liquid crystal into a Ch shell and an isotropic core is preserved in flexible capillary tubing, suggesting the applicability of this system for the fabrication of flexible optical waveguides.