  We establish a link between metastability and a discrete time-crystalline
phase in a periodically driven open quantum system. The mechanism we highlight
requires neither the system to display any microscopic symmetry nor the
presence of disorder, but relies instead on the emergence of a metastable
regime. We investigate this in detail in an open quantum spin system, which is
a canonical model for the exploration of collective phenomena in strongly
interacting dissipative Rydberg gases. Here, a semi-classical approach reveals
the emergence of a robust discrete time-crystalline phase in the thermodynamic
limit in which metastability, dissipation, and inter-particle interactions play
a crucial role. We perform large-scale numerical simulations in order to
investigate the dependence on the range of interactions, from all-to-all to
short ranged, and the scaling with system size of the lifetime of the time
crystal.
