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We propose a class of synthetic optical materials in which the refractive index satisfies n(−x)=−n*(x). We term such systems antisymmetric parity-time () structures. Unlike -symmetric systems, which require balanced gain and loss, i.e., n(−x)=n*(x), systems consist of balanced positive- and negative-index materials. Despite the seemingly -symmetric optical potential V(x)≡n(x)2ω2/c2, systems are not invariant under combined operations due to the discontinuity of the spatial derivative of the wave function. We show that systems can display intriguing properties, such as spontaneous phase transition of the scattering matrix, a flat total transmission band, and a continuous lasing spectrum.