  We report the serendipitous discovery of a quadruply lensed source at $z_{\rm
s}=3.76$, HSC~J115252+004733, from the Hyper Suprime-Cam (HSC) Survey. The
source is lensed by an early-type galaxy at $z_{\rm l}=0.466$ and a satellite
galaxy. Here, we investigate the properties of the source by studying its size
and luminosity from the imaging and the luminosity and velocity width of the
Ly-$\alpha$ line from the spectrum. Our analyses suggest that the source is
most probably a low-luminosity active galactic nucleus (LLAGN) but the
possibility of it being a compact bright galaxy (e.g., a Lyman-$\alpha$ emitter
or Lyman Break Galaxy) cannot be excluded. The brighter pair of lensed images
appears point-like except in the HSC $i$-band (with a seeing $\sim0.5"$). The
extended emission in the $i$-band image could be due to the host galaxy
underneath the AGN, or alternatively, due to a highly compact lensed galaxy
(without AGN) which appears point-like in all bands except in $i$-band. We also
find that the flux ratio of the brighter pair of images is different in the
Ks-band compared to optical wavelengths. Phenomena such as differential
extinction and intrinsic variability cannot explain this chromatic variation.
While microlensing from stars in the foreground galaxy is less likely to be the
cause, it cannot be ruled out completely. If the galaxy hosts an AGN, then this
represents the highest redshift quadruply imaged AGN known to date, enabling
study of a distant LLAGN. Discovery of this unusually compact and faint source
demonstrates the potential of the HSC survey.
