We report the serendipitous discovery of HSC J0904$-$0102, a quadruply-lensed Lyman break galaxy (LBG) in the Survey of Gravitationally-lensed Objects in Hyper Suprime-Cam Imaging (SuGOHI). Owing to its point-like appearance, the source was thought to be a lensed active galactic nucleus. We obtained follow-up spectroscopic data with the Gemini Multi-Object Spectrographs on the Gemini South Telescope, which confirmed this to be a lens system. The deflecting foreground galaxy is a typical early-type galaxy at a high redshift of $z_{ell} = 0.957$ with stellar velocity dispersion $sigma_v=259pm56$ km~s$^{-1}$. The lensed source is identified as an LBG at $z_{rm s} = 3.403$, based on the sharp drop bluewards of Ly$alpha$ and other absorption features. A simple lens mass model for the system, assuming a singular isothermal ellipsoid, yields an Einstein radius of $theta_{rm Ein} = 1. 23^{primeprime}$ and a total mass within the Einstein radius of $M_{rm Ein} = (5.55pm 0.24) times 10^{11}M_{odot}$ corresponding to a velocity dispersion of $sigma_{rm SIE}= 283pm 3$ km~s$^{-1}$, which is in good agreement with the value derived spectroscopically. The most isolated lensed LBG image has a magnification of $sim 6.5$. In comparison with other lensed LBGs and typical $zsim4$ LBG populations, HSC J0904$-$0102 is unusually compact, an outlier at $>2sigma$ confidence. Together with a previously discovered SuGOHI lens, HSC J1152$+$0047, that is similarly compact, we believe that the HSC Survey is extending LBG studies down to smaller galaxy sizes.
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