We conduct the first numerical simulations of lattice theories with exact supersymmetry arising from the orbifold constructions of Cohen:2003xe,Cohen:2003qw,Kaplan:2005ta. We consider the =4 theory in D=0,2 dimensions and the =16 theory in D=0,2,4 dimensions. We show that the U(N) theories do not possess vacua which are stable non-perturbatively, but that this problem can be circumvented after truncation to SU(N). We measure the distribution of scalar field eigenvalues, the spectrum of the

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... on operator and the phase of the Pfaffian arising after integration over the fermions. We monitor supersymmetry breaking effects by measuring a simple Ward identity. Our results indicate that simulations of N=4 super Yang-Mills may be achievable in the near future.