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.
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