  We report on the search for electromagnetic counterparts to the nine
gravitational-wave events with a $>$60\% probability of containing a neutron
star during the third (O3) LIGO-Virgo Collaboration (LVC) observing run with
the All-Sky Automated Survey for SuperNovae (ASAS-SN). No optical counterparts
associated with a gravitational wave event was found. However, thanks to its
network of telescopes, the average area visible to at least one ASAS-SN site
during the first 10 hours after the trigger contained $\sim$30\% of the
integrated source location probability. Through a combination of normal
operations and target-of-opportunity observations, ASAS-SN observations of the
highest probability fields began within one hour of the trigger for four of the
events. After 24 hours, ASAS-SN observed $>$60\% of total probability for three
events and $>$40\% for all but one of the events. This is the largest area
coverage to a depth of $g = 18.5$ mag from any survey with published coverage
statistics for seven of the nine events. With its observing strategy, five
sites around the world, and a large field of view, ASAS-SN will be one of the
leading surveys to optically search for nearby neutron star mergers during LVC
O4.
