We construct N=1 supersymmetric fractional branes on the Z_6' orientifold. Intersecting stacks of such branes are needed to build a supersymmetric standard model. If $a,b$ are the stacks that generate the SU(3)_c and SU(2)_L gauge particles, then, in order to obtain just the chiral spectrum of the (supersymmetric) standard model (with non-zero Yukawa couplings to the Higgs mutiplets), it is necessary that the number of intersections a \cap b of the stacks a and b, and the number of intersections a \cap b' of a with the orientifold image b' of b satisfy (a \cap b,a \cap b')=(2,1) or (1,2). It is also necessary that there is no matter in symmetric representations of either gauge group. We have found a number of examples having these properties.

4 pages. To appear in Proceedings of SUSY06, the 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions, UC Irvine, California, 12-17 June 2006