  Laboratory optical atomic clocks achieve remarkable accuracy (now counted to
18 digits or more), opening possibilities to explore fundamental physics and
enable new measurements. However, their size and use of bulk components prevent
them from being more widely adopted in applications that require precision
timing. By leveraging silicon-chip photonics for integration and to reduce
component size and complexity, we demonstrate a compact optical-clock
architecture. Here a semiconductor laser is stabilized to an optical transition
in a microfabricated rubidium vapor cell, and a pair of interlocked
Kerr-microresonator frequency combs provide fully coherent optical division of
the clock laser to generate an electronic 22 GHz clock signal with a fractional
frequency instability of one part in 10^13. These results demonstrate key
concepts of how to use silicon-chip devices in future portable and ultraprecise
optical clocks.
