A new orientifold of Type-IIB theory on K3 is constructed that has N=1 supersymmetry in six dimensions. The orientifold symmetry consists of a Z_2 involution of K3 combined with orientation-reversal on the worldsheet. The closed-string sector in the resulting theory contains nine tensor multiplets and twelve neutral hypermultiplets in addition to the gravity multiplet, and is anomaly-free by itself. The open-string sector contains only 5-branes and gives rise to maximal gauge groups SO(16) or

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... 8)× U(8) at different points in the moduli space. Anomalies are canceled by a generalization of the Green-Schwarz mechanism that involves more than one tensor multiplets.