  Supersymmetric Yang-Mills (SYM) theories in four dimensions exhibit many
interesting non-perturbative phenomena that can be studied by means of Monte
Carlo lattice simulations. However, the lattice regularization breaks
supersymmetry explicitly, and in general a fine tuning of a large number of
parameters is required to correctly extrapolate the theory to the continuum
limit. From this perspective, it is important to preserve on the lattice as
many symmetries of the original continuum action as possible. Chiral symmetry
for instance prevents an additive renormalization of the fermion mass. A
(modified) version of chiral symmetry can be preserved exactly if the Dirac
operator fulfills the Ginsparg-Wilson relation. In this contribution, we
present an exploratory non-perturbative study of N=1 supersymmetric Yang-Mills
theory using the overlap formalism to preserve chiral symmetry at non-zero
lattice spacings. N=1 SYM is an ideal benchmark toward the extension of our
studies to more complex supersymmetric theories, as the only parameter to be
tuned is the gluino mass. Overlap fermions allow therefore to simulate the
theory without fine-tuning. We compare our approach to previous investigations
of the same theory, and we present clear evidences for gluino condensation.
