  We investigate the dynamics of a Bose-Einstein condensate interacting with
two non-interfering and counterpropagating modes of a ring resonator.
Superfluid, supersolid and dynamic phases are identified experimentally and
theoretically. The supersolid phase is obtained for sufficiently equal pump
strengths for the two modes. In this regime we observe the emergence of a
steady state with crystalline order, which spontaneously breaks the continuous
translational symmetry of the system. The supersolidity of this state is
demonstrated by the conservation of global phase coherence at the superfluid to
supersolid phase transition. Above a critical pump asymmetry the system evolves
into a dynamic run-away instability commonly known as collective atomic recoil
lasing. We present a phase diagram and characterize the individual phases by
comparing theoretical predictions with experimental observations.
