  We report the discovery of a highly-polarized, highly-variable,
steep-spectrum radio source, ASKAP J173608.2-321635, located $\sim$4\,deg from
the Galactic center in the Galactic plane. The source was detected six times
between 2020 January and 2020 September as part of the Australian Square
Kilometre Array Pathfinder Variables and Slow Transients (ASKAP VAST) survey at
888\,MHz. It exhibited a high degree ($\sim 25$\%) of circular polarization
when it was visible. We monitored the source with the MeerKAT telescope from
2020 November to 2021 February on a 2--4 week cadence. The source was not
detected with MeerKAT before 2021 February 07 when it appeared and reached a
peak flux density of 5.6\,mJy. The source was still highly circularly
polarized, but also showed up to 80\% linear polarization, and then faded
rapidly with a timescale of one day. The rotation measure of the source varied
significantly, from $-11.8\pm0.8$\,rad\,m$^{-2}$ to
$-64.0\pm1.5$\,rad\,m$^{-2}$, over three days. No X-ray counterpart was found
in follow-up \textit{Swift} or \textit{Chandra} observations about a week after
the first MeerKAT detection, with upper limits of $\sim
5.0\times10^{31}$\,erg\,s$^{-1}$ (0.3--8\,keV, assuming a distance $\sim10$
kpc). No counterpart is seen in new or archival near-infrared observations down
to $J=20.8$\,mag. We discuss possible identifications for ASKAP
J173608.2-321635 including a low-mass star/substellar object with extremely low
infrared luminosity, a pulsar with scatter-broadened pulses, a transient
magnetar, or a Galactic Center Radio Transient: none of these fully explains
the observations, which suggests that ASKAP J173608.2-321635 may represent part
of a new class of objects being discovered through radio imaging surveys.
