We present Keck Cosmic Web Imager spectroscopy of the four putative images of the lensed quasar candidate J014709+463037 recently discovered by Berghea et al. (2017). The data verify the source as a quadruply lensed, broad absorption-line quasar having z_S = 2.377 +/- 0.007. We detect intervening absorption in the FeII 2586, 2600, MgII 2796, 2803, and/or CIV 1548, 1550 transitions in eight foreground systems, three of which have redshifts consistent with the photometric-redshift estimate reported for the lensing galaxy (z_L ~ 0.57). By virtue of their positions on the sky, the source images probe these absorbers over transverse physical scales of ~0.3-21 kpc, permitting assessment of the variation in metal-line equivalent width W_r as a function of sight-line separation. We measure differences in W_r,2796 of <40% across all sight-line pairs subtending 7-21 kpc, suggestive of a high degree of spatial coherence for MgII-absorbing material. W_r,2600 is observed to vary by >50% over the same scales across the majority of sight-line pairs, while CIV absorption exhibits a wide range in W_r,1548 differences of ~5-80% within transverse distances less than ~3 kpc. J014709+463037 is one of only a handful of z > 2 quadruply lensed systems for which all four source images are very bright (r = 15.4-17.7 mag) and are easily separated in ground-based seeing conditions. As such, it is an ideal candidate for higher-resolution spectroscopy probing the spatial variation in the kinematic structure and physical state of intervening absorbers.
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