Optical atomic clocks play a crucial role in fundamental physics, relativistic geodesy, and the future redefinition of the Systeme International second. Standard operation relies on cyclic interrogation sequences, which alternate between atomic interrogation and dead time used for state preparation and readout. This approach introduces the Dick effect, where laser frequency noise aliases onto the atomic transition frequency. Although reducing laser noise improves clock stability, the Dick effect remains a key limitation. In this Letter, we demonstrate a zero-dead-time optical clock based on two interleaved ensembles of cold ${}^{87}\mathrm{Sr}$ atoms. Our system significantly suppresses this noise and achieves a fractional frequency instability at the ${10}^{-19}$ level between 10 000 and 20 000 s over repeated measurements, with a best value of $2.9\times {10}^{-19}$ at $\tau =20000\mathrm{s}$. The estimated long-term stability based on the combined data of these measurements reaches $2.5\times {10}^{-19}$ at 1 day. These results represent a more than ninefold improvement over a conventional single-ensemble clock, highlighting its potential for next-generation timekeeping applications.

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• Atomic, optical & lattice clocks