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Layered heterostructures combining ordinary and negative refractive index materials are shown to display a new type of photonic band gap corresponding to zero (volume) averaged refractive index. Distinct from band gaps induced by Bragg scattering, the zero- gap is invariant upon a change of scale length and is insensitive to disorder that is symmetric in the random variable. A metallic structure that exhibits such a band gap is explicitly designed, and its properties are calculated with accurate finite difference time domain simulations.