We report on the formation of unprecedented "leek"-shaped aggregates of an anionic fluoroalkyl sulfonate surfactant (FS) and the supramolecular assembly of these aggregates into a disordered columnar phase (C-s). The leeks are formed by wrapping of 2-4 FS water bilayers of thickness 26-28 A into 10-20 nm thick and >100 nm long structures, in the concentration regime of 63-70 wt % FS. A lamellar (L-alpha) lyotropic liquid-crystalline (LLC) phase forms at higher concentration, between 70 and 84 wt %. In the two LLC phases, the FS molecules were organized in an interdigitated or tilted fashion, or a combination of the two. Such a unique supramolecular self-assembly of amphiphiles has not been predicted nor observed before. This self-assembly behavior could be of interest to various fields like microencapsulation, nanomedicine, and membrane protein crystallization.