  LIGO's mission critical timing system has enabled gravitational wave and
multi-messenger astrophysical discoveries as well as the rich science
extracted. Achieving optimal detector sensitivity, detecting transient
gravitational waves, and especially localizing gravitational wave sources, the
underpinning of multi-messenger astrophysics, all require proper gravitational
wave data time-stamping. Measurements of the relative arrival times of
gravitational waves between different detectors allow for coherent
gravitational wave detections, localization of gravitational wave sources, and
the creation of skymaps. The carefully designed timing system achieves these
goals by mitigating phase noise to avoid signal up-conversion and maximize
gravitational wave detector sensitivity. The timing system also redundantly
performs self-calibration and self-diagnostics in order to ensure reliable,
extendable, and traceable time stamping. In this paper, we describe and
quantify the performance of these core systems during the latest O3 scientific
run of LIGO, Virgo, and KAGRA. We present results of the diagnostic checks done
to verify the time-stamping for individual gravitational wave events observed
during O3 as well as the timing system performance for all of O3 in LIGO
Livingston and LIGO Hanford. We find that, after 3 observing runs, the LIGO
timing system continues to reliably meet mission requirements of timing
precision below 1 $\mu$s with a significant safety margin.
