This paper presents a study of the galactic environment of a chemically-pristine (<0.6% solar metallicity) Lyman Limit system (LLS) discovered along the sightline toward QSO SDSSJ135726.27+043541.4 (zQSO=1.233) at projected distance d=126 physical kpc (pkpc) from a luminous red galaxy (LRG) at z=0.33. Combining deep Hubble Space Telescope images, MUSE integral field spectroscopic data, and wide-field redshift survey data has enabled an unprecedented, ultra-deep view of the environment around this LRG-LLS pair. A total of 12 galaxies, including the LRG, are found at d<~400 pkpc and line-of-sight velocity dv<600 km/s of the LLS, with intrinsic luminosity ranging from 0.001L* to 2L* and a corresponding stellar mass range of Mstar=10^{7-11} Msun. All 12 galaxies contribute to a total mass of Mstar=1.6e11 Msun with ~80% contained in the LRG. The line-of-sight velocity dispersion of these galaxies is found to be {sigma}_group=230 km/s with the center of mass at d_group=118 pkpc and line-of-sight velocity offset of {Delta}v_group=181 km/s from the LLS. Three of these are located at d<~100 pkpc from the LLS, and they are all faint with intrinsic luminosity <0.02 L* and gas phase metallicity of ~10% solar in their interstellar medium. The disparity in the chemical enrichment level between the LLS and the group members suggests that the LLS originates in infalling intergalactic medium and that parts of the intergalactic gas near old and massive galaxies can still remain chemically pristine through the not too distant past.
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