  We demonstrate the possibility of a stable equilibrium multi-lamellar
(``onion'') phase in pure lamellar systems (no excess solvent) due to a
sufficiently negative Gaussian curvature modulus. The onion phase is stabilized
by non-linear elastic moduli coupled to a polydisperse size distribution
(Apollonian packing) to allow space-filling without appreciable elastic
distortion. This model is compared to experiments on copolymer-decorated
lamellar surfactant systems, with reasonable qualitative agreement.
