We find that the relative contribution of satellite galaxies accreted at high redshift to the stellar population of the Milky Way's smooth halo increases with distance, becoming observable relative to the classical smooth halo about 15 kpc from the Galactic center. In particular, we determine line-of-sight-averaged [Fe/H] and [α/Fe] in the metal-poor main-sequence turnoff (MPMSTO) population along every Sloan Extension for Galactic Understanding and Exploration (SEGUE) spectroscopic line of sight. Restricting our sample to those lines of sight along which we do not detect elements of cold halo substructure (ECHOS), we compile the largest spectroscopic sample of stars in the smooth component of the halo ever observed in situ beyond 10 kpc. We find significant spatial autocorrelation in [Fe/H] in the MPMSTO population in the distant half of our sample beyond about 15 kpc from the Galactic center. Inside of 15 kpc however, we find no significant spatial autocorrelation in [Fe/H]. At the same time, we perform SEGUE-like observations of N-body simulations of Milky Way analog formation. While we find that halos formed entirely by accreted satellite galaxies provide a poor match to our observations of the halo within 15 kpc of the Galactic center, we do observe spatial autocorrelation in [Fe/H] in the simulations at larger distances. This observation is an example of statistical chemical tagging and indicates that spatial autocorrelation in metallicity is a generic feature of stellar halos formed from accreted satellite galaxies.