  We construct N=1 supersymmetric four-dimensional orientifolds of type IIA on
T^6/(Z_2 x Z_2) with D6-branes intersecting at angles. The use of D6-branes not
fully aligned with the O6-planes in the model allows for a construction of many
supersymmetric models with chiral matter, including those with the Standard
Model and grand unified gauge groups. We perform a search for realistic gauge
sectors, and construct the first example of a supersymmetric type II
orientifold with SU(3)_C x SU(2)_L x U(1)_Y gauge group and three quark-lepton
families. In addition to the supersymmetric Standard Model content, the model
contains right-handed neutrinos, a (chiral but anomaly-free) set of exotic
multiplets, and diverse vector-like multiplets. The general class of these
constructions are related to familiar type II orientifolds by small instanton
transitions, which in some cases change the number of generations, as discussed
in specific models. These constructions are supersymmetric only for special
choices of untwisted moduli. We briefly discuss the supersymmetry breaking
effects away from that point. The M-theory lift of this general class of
supersymmetric orientifold models should correspond to purely geometrical
backgrounds admitting a singular G_2 holonomy metric and leading to
four-dimensional M-theory vacua with chiral fermions.
