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We demonstrate a non-equilibrium phase transition in a dilute thermal atomicgas. The phase transition, between states of low and high Rydberg occupancy, isinduced by resonant dipole-dipole interactions between Rydberg atoms. The gascan be considered as dilute as the atoms are separated by distances muchgreater than the wavelength of the optical transitions used to excite them. Inthe frequency domain we observe a mean-field shift of the Rydberg state whichresults in intrinsic optical bistability above a critical Rydberg numberdensity. In the time domain we observe critical slowing down where the recoverytime to system perturbations diverges with critical exponent  $\tau=0.53 \pm 0.10$. The atomic emission spectrum of the phase with highRydberg occupancy provides evidence for a superradiant cascade.

Cooperative non-equilibrium phase transition in a dilute Rydberg ensemble