  We show that a two-dimensional atomic mixture of Bosons and Fermions cooled
into their quantum degenerate states and subject to an optical lattice develops
a supersolid phase characterized by the simultaneous presence of a non-trivial
crystalline order and phase order. This transition is in competition with a
phase separated ground state. We determine the phase diagram of the system and
propose an experiment allowing for the observation of the supersolid phase.
