  Condensed matter physics has been driven forward by significant experimental
and theoretical progress in the study and understanding of equilibrium phase
transitions based on symmetry and topology. However, nonequilibrium phase
transitions have remained a challenge, in part due to their complexity in
theoretical descriptions and the additional experimental difficulties in
systematically controlling systems out of equilibrium. Here, we study a
one-dimensional chain of 72 microwave cavities, each coupled to a
superconducting qubit, and coherently drive the system into a nonequilibrium
steady state. We find experimental evidence for a dissipative phase transition
in the system in which the steady state changes dramatically as the mean photon
number is increased. Near the boundary between the two observed phases, the
system demonstrates bistability, with characteristic switching times as long as
60 ms -- far longer than any of the intrinsic rates known for the system. This
experiment demonstrates the power of circuit QED systems for studying
nonequilibrium condensed matter physics and paves the way for future
experiments exploring nonequilbrium physics with many-body quantum optics.
