  Optical atomic clocks have demonstrated revolutionary advances in precision
timekeeping, but their applicability to the real world is critically dependent
on whether such clocks can operate outside a laboratory setting. The challenge
to clock portability stems from the many obstacles not only in miniaturizing
the underlying components of the clock $-$ namely the ultrastable laser, the
frequency comb, and the atomic reference itself $-$ but also in making the
clock resilient to environmental fluctuations. Photonic integration offers one
compelling solution to simultaneously address the problems of miniaturization
and ruggedization, but brings with it a new set of challenges in recreating the
functionality of an optical clock using chip-scale building blocks. The clock
laser used for atom interrogation is one particular point of uncertainty, as
the performance of the meticulously-engineered bulk-cavity stabilized lasers
would be exceptionally difficult to transfer to chip. Here we demonstrate that
a chip-integrated ultrahigh quality factor (Q) spiral cavity, when interfaced
with a 1348 nm seed laser, reaches a fractional frequency instability of $7.5
\times 10^{-14}$, meeting the stability requirements for interrogating the
narrow-linewidth transition of $^{88}$Sr$^+$ upon frequency doubling to 674 nm.
In addition to achieving the record for laser stability on chip, we use this
laser to showcase the operation of a Sr-ion clock with short-term instability
averaging down as $3.9 \times 10^{-14} / \sqrt{\tau}$, where $\tau$ is the
averaging time. Our demonstration of an optical atomic clock interrogated by an
integrated spiral cavity laser opens the door for future advanced clock systems
to be entirely constructed using lightweight, portable, and mass-manufacturable
integrated optics and electronics.
