There has been a fundamental flaw in all previous attempts to put supersymmetry on the lattice. Because supersymmetry closes on the Poincare group, and since the Wilson lattice breaks Poincare invariance, the standard lattice must necessarily break supersymmetry. We solve this difficulty by putting supersymmetry on a random super lattice, where each random site is a point in super space (x/sub i/,xi/sub i/). We construct the action out of unitary SU(N) superfields connecting two such super lattice sites and sum the traces over simplexes. The theory is manifestly supersymmetric because there is no preferred direction in either real or Grassmann space. This supersymmetric lattice gauge theory on a random lattice reduces to the usual supersymmetric gauge theory in the continuum limit. We discuss applications, such as calculating nonperturbative corrections to the vacuum energy, which may yield a large enough supersymmetry breaking to explain the hierarchy problem. We discuss using random lattices to describe a lattice version of gravity and supergravity.