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We report the serendipitous discovery of a quadruply lensed source at $z_{\rms}=3.76$, HSC~J115252+004733, from the Hyper Suprime-Cam (HSC) Survey. Thesource is lensed by an early-type galaxy at $z_{\rm l}=0.466$ and a satellitegalaxy. Here, we investigate the properties of the source by studying its sizeand luminosity from the imaging and the luminosity and velocity width of theLy-$\alpha$ line from the spectrum. Our analyses suggest that the source ismost probably a low-luminosity active galactic nucleus (LLAGN) but thepossibility of it being a compact bright galaxy (e.g., a Lyman-$\alpha$ emitteror Lyman Break Galaxy) cannot be excluded. The brighter pair of lensed imagesappears point-like except in the HSC $i$-band (with a seeing $\sim0.5"$). Theextended emission in the $i$-band image could be due to the host galaxyunderneath 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 alsofind that the flux ratio of the brighter pair of images is different in theKs-band compared to optical wavelengths. Phenomena such as differentialextinction and intrinsic variability cannot explain this chromatic variation.While microlensing from stars in the foreground galaxy is less likely to be thecause, it cannot be ruled out completely. If the galaxy hosts an AGN, then thisrepresents the highest redshift quadruply imaged AGN known to date, enablingstudy of a distant LLAGN. Discovery of this unusually compact and faint sourcedemonstrates the potential of the HSC survey.

A new quadruple gravitational lens from the Hyper Suprime-Cam Survey: the puzzle of HSC~J115252+004733