Acid hydrolysis of cellulose fibers produces suspensions of colloidal cellulose nanocrystals. At low concentrations these suspensions are isotropic, while at high concentrations the cellulose rods spontaneously organize into a chiral nematic liquid crystal phase. We have studied the effect of adding high molecular weight dextran to various concentrations of these cellulose suspensions. Adding dextran to an isotropic suspension caused no demixing of the two components. When dextran was added to a biphasic sample, it preferentially partitioned into the isotropic phase. Adding dextran to a completely anisotropic phase caused a phase separation into a dextran-rich isotropic phase and a dextran-poor anisotropic phase. The incorporation of dextran in the chiral nematic phase caused a marked increase in defects in the liquid crystalline texture.