  The infrared effective theory of adjoint QCD with one Dirac flavour is still
under debate. The theory could be confining, conformal, or with a massless
fermion in the infrared. The study of chiral symmetry seems to be important to
answer this question. While previous investigations have considered Wilson
fermions, we present here the first results for this theory based on overlap
fermions to avoid explicit chiral symmetry breaking. These indicate spontaneous
chiral symmetry breaking by the formation of a fermion condensate. We have also
investigated the running coupling of the theory, which indicates no infrared
conformality in the energy region we have explored.
