Spectroscopy of background QSO sightlines passing close to foreground galaxies is a potent technique for studying the circumgalactic medium (CGM). QSOs are effectively point sources, however, limiting their potential to constrain the size of circumgalactic gaseous structures. Here we present the first large Keck/LRIS and VLT/FORS2 spectroscopic survey of bright (B_AB < 22.3) background galaxies whose lines of sight probe MgII 2796, 2803 absorption from the CGM around close projected foreground galaxies at transverse distances 10 kpc < R_perp < 150 kpc. Our sample of 72 projected pairs, drawn from the PRIsm MUlti-object Survey (PRIMUS), includes 48 background galaxies which do not host bright AGN, and both star-forming and quiescent foreground galaxies with stellar masses 9.0 < log M_*/M_sun < 11.2 at redshifts 0.35 < z_f/g < 0.8. We detect MgII absorption associated with these foreground galaxies with equivalent widths 0.25 Ang < W_2796 < 2.6 Ang at >2sigma significance in 20 individual background sightlines passing within R_perp < 50 kpc, and place 2sigma upper limits on W_2796 of <0.5 Ang in an additional 11 close sightlines. Within R_perp < 50 kpc, W_2796 is anticorrelated with R_perp, consistent with analyses of MgII absorption detected along background QSO sightlines. Subsamples of these foreground hosts divided at log M_*/M_sun = 9.9 exhibit statistically inconsistent W_2796 distributions at 30 kpc < R_perp < 50 kpc, with the higher-M_* galaxies yielding a larger median W_2796 by 0.9 Ang. Finally, we demonstrate that foreground galaxies with similar stellar masses exhibit the same median W_2796 at a given R_perp to within <0.2 Ang toward both background galaxies and toward QSO sightlines drawn from the literature. Analysis of these datasets constraining the spatial coherence scale of circumgalactic MgII absorption is presented in a companion paper.
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