  Time crystals are classified as discrete or continuous depending on whether
they spontaneously break discrete or continuous time translation symmetry.
While discrete time crystals have been extensively studied in periodically
driven systems since their recent discovery, the experimental realization of a
continuous time crystal is still pending. Here, we report the observation of a
limit cycle phase in a continuously pumped dissipative atom-cavity system,
which is characterized by emergent oscillations in the intracavity photon
number. We observe that the phase of this oscillation is random for different
realizations, and hence this dynamical many-body state breaks continuous time
translation symmetry spontaneously. The observed robustness of the limit cycles
against temporal perturbations confirms the realization of a continuous time
crystal.
