The circumgalactic medium (CGM) close to ~L* star-forming galaxies hosts strong MgII 2796 absorption (with equivalent width W_2796>0.1 Ang) with a near-unity covering fraction. To characterize the spatial coherence of this absorption, we analyze the W_2796 distribution in the CGM of 27 star-forming galaxies detected in deep spectroscopy of bright background (b/g) galaxies first presented in Rubin et al. (2018). The sample foreground (f/g) systems have redshifts 0.35<z<0.8 and stellar masses 9.1<log M_*/M_sun<11.1, and the b/g galaxies provide spatially-extended probes with half-light radii 1.0 kpc<R_eff<7.9 kpc at projected distances R_perp<50 kpc. Our analysis also draws on literature W_2796 values measured in b/g QSO spectroscopy probing the halos of f/g galaxies with a similar range in M_* at z ~ 0.25. By making the assumptions that (1) samples of like galaxies exhibit similar circumgalactic W_2796 distributions; and that (2) the quantity log W_2796 has a Gaussian distribution with a dispersion that is constant with M_* and R_perp, we use this QSO-galaxy pair sample to construct a model for the log W_2796 distribution in the CGM. We then demonstrate the dependence of this distribution on the ratio of the surface area of the b/g probe to the projected absorber surface area (x_A=A_G/A_A), finding that distributions which assume x_A>=15 are statistically inconsistent with that observed toward our b/g galaxies at a 95% confidence level. This limit, in combination with the b/g galaxy sizes, requires that the length scale over which W_2796 does not vary (the coherence scale of MgII absorption) is l_A>1.9 kpc. This novel constraint on the morphology of cool, photoionized structures in the inner CGM suggests that either these structures each extend over kiloparsec scales, or that the numbers and velocity dispersion of these structures are spatially correlated over the same scales.
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