In the phase diagram of the surfactant system sodium oleate/octanol/water a very stiff gel phase has been found, which is usually not present in similar systems. The phases of this system have been characterized by electric conductivity and rheological measurements. The structures present have been investigated by means of freeze-fracture electron microscopy and small-angle neutron scattering (SANS). These experiments have shown that addition of octanol to the surfactant solution for concentrations higher than 130 mM Na oleate leads to the formation of small unilamellar vesicles. For sufficiently high octanol content these vesicles are so monodisperse that they are able to form a densely packed system with long-range order and with a shear modulus that is about 100 times higher than normally found for vesicle systems. Upon dilution with water the vesicles swell while keeping the packing fraction constant until a maximum diameter of about 450 Angstrom is reached, beyond which no further growth of the vesicles can take place. This is the first system of such type that forms a cubic-phase-like arrangement of monodisperse vesicles.