The formation of a phase of matter can be associated with the spontaneous breaking of a symmetry. For crystallization, this broken symmetry is the spatial translation symmetry, as the atoms spontaneously localize in a periodic fashion. In analogy to spatial crystals, the spontaneous breaking of temporal translation symmetry results in the formation of time crystals. While recent and on-going experiments on driven isolated systems aim to minimize dissipative processes, as it is an undesired source of decay, well-designed dissipation has been put forth as a constitutive ingredient in the formation of dissipative time crystals (DTCs). Here, we present the first experimental realisation of a DTC, implemented in an atom-cavity system. Its defining feature is a period doubled switching between distinct chequerboard density wave patterns, induced by controlled cavity-dissipation and cavity-mediated interactions. We demonstrate the robustness of this phase against system parameter changes and temporal perturbations of the driving. Our work provides a framework for realising phases of matter with spatiotemporal order in presence of dissipation. We note that this is the natural environment of matter, and therefore shapes its physical phenomena profoundly, making its study imperative.
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