This paper reports the experimental realization of the Dicke quantum phase transition in a Bose-Einstein condensate (BEC) coupled to an optical cavity. The transition is driven by long-range interactions between the atoms, induced by two-photon processes involving the cavity mode and a pump field. The system exhibits a self-organized supersolid phase, where the spatial symmetry of the lattice is spontaneously broken. The phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and is quantitatively consistent with the Dicke model. The boundary of the phase transition is mapped out, showing a sharp phase boundary over a wide range of pump-cavity detuning. The work opens the field of quantum gases with long-range interactions and provides access to novel quantum phases. The experiment involves a BEC trapped in an ultrahigh-finesse optical cavity, pumped from a direction transverse to the cavity axis. The system is observed to self-organize into a checkerboard pattern, with the cavity field and atomic polarization acquiring macroscopic occupations. The phase transition is accompanied by spontaneous symmetry breaking in the atomic density and the relative phase between the pump field and cavity field. The results demonstrate that the process of self-organization is equivalent to the Dicke quantum phase transition in an open system. The cavity output field allows for in-situ monitoring of the phase transition and extraction of important system properties. The study provides experimental access to the phase diagram of the Dicke model and highlights the potential for studying coherent dynamics of the Dicke model at the critical point, dominated by macroscopic atom-field and atom-atom entanglement. The work also opens opportunities for studying spontaneous symmetry breaking induced by quantum fluctuations and quantum non-demolition measurements.This paper reports the experimental realization of the Dicke quantum phase transition in a Bose-Einstein condensate (BEC) coupled to an optical cavity. The transition is driven by long-range interactions between the atoms, induced by two-photon processes involving the cavity mode and a pump field. The system exhibits a self-organized supersolid phase, where the spatial symmetry of the lattice is spontaneously broken. The phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and is quantitatively consistent with the Dicke model. The boundary of the phase transition is mapped out, showing a sharp phase boundary over a wide range of pump-cavity detuning. The work opens the field of quantum gases with long-range interactions and provides access to novel quantum phases. The experiment involves a BEC trapped in an ultrahigh-finesse optical cavity, pumped from a direction transverse to the cavity axis. The system is observed to self-organize into a checkerboard pattern, with the cavity field and atomic polarization acquiring macroscopic occupations. The phase transition is accompanied by spontaneous symmetry breaking in the atomic density and the relative phase between the pump field and cavity field. The results demonstrate that the process of self-organization is equivalent to the Dicke quantum phase transition in an open system. The cavity output field allows for in-situ monitoring of the phase transition and extraction of important system properties. The study provides experimental access to the phase diagram of the Dicke model and highlights the potential for studying coherent dynamics of the Dicke model at the critical point, dominated by macroscopic atom-field and atom-atom entanglement. The work also opens opportunities for studying spontaneous symmetry breaking induced by quantum fluctuations and quantum non-demolition measurements.