  We construct a lattice theory with one exact supersymmetry which consists of
fields transforming in both the adjoint and fundamental representations of a
U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf
flavors of fermion in the fundamental representation along with their scalar
partners and is invariant under a global U(Nf) flavor symmetry. The lattice
action contains an additional Fayet-Iliopoulos term which can be used to
generate a scalar potential. We perform numerical simulations that corroborate
the theoretical expectation that supersymmetry is spontaneously broken for
Nf<Nc.
