Levan, which adopts a compact spherical conformation in aqueous solution, can form a liquid crystalline phase if DNA is also present. We propose that supramolecular rodlike structures, assembled by the noncovalent aggregation of levan around DNA, stabilize the lyotropic phase. We describe a geometric model for the aggregates. The model is quantitatively consistent with the relative amounts of DNA and levan needed for liquid crystallinity, and it agrees qualitatively with the shape of the boundary between the isotropic and heterogeneous fields on an experimentally determined phase diagram.[S0031-9007 (97)05063-1] PACS numbers: 87.15.Da, 36.20.Fz, 61.25.Hq, 64.70.Md