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We report on a broad new class of N=1 gauge theory dualities which relate theworldvolume gauge theories of D3 branes probing different orientifolds of thesame Calabi-Yau singularity. In this paper, we focus on the simplest example ofthese new dualities, arising from the orbifold singularity C^3/Z_3. We presentextensive checks of the duality, including anomaly matching, partial modulispace matching, matching of discrete symmetries, and matching of thesuperconformal indices between the proposed duals. We then present a relatedduality for the dP_1 singularity, as well as dualities for the F_0 and Y^{4,0}singularities, illustrating the breadth of this new class of dualities. In acompanion paper, we show that certain infinite classes of geometries whichinclude C^3/Z_3 and dP_1 all exhibit such dualities, and argue that theirten-dimensional origin is the SL(2,Z) self-duality of type IIB string theory.

New N=1 dualities from orientifold transitions - Part I: Field Theory