The authors realize a quantum phase transition in a Bose-Einstein condensate (BEC) coupled to an optical cavity, demonstrating the emergence of a self-organized supersolid phase. This transition is driven by infinitely long-range interactions between condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. The phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and the supersolid phase is associated with spontaneous breaking of spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model, providing access to novel quantum phases in systems with long-range interactions.The authors realize a quantum phase transition in a Bose-Einstein condensate (BEC) coupled to an optical cavity, demonstrating the emergence of a self-organized supersolid phase. This transition is driven by infinitely long-range interactions between condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. The phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and the supersolid phase is associated with spontaneous breaking of spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model, providing access to novel quantum phases in systems with long-range interactions.