  We determine the average metallicities of the elements of cold halo
substructure (ECHOS) that we previously identified in the inner halo of the
Milky Way within 17.5 kpc of the Sun. As a population, we find that stars
kinematically associated with ECHOS are chemically distinct from the background
kinematically smooth inner halo stellar population along the same Sloan
Extension for Galactic Understanding and Exploration (SEGUE) line of sight.
ECHOS are systematically more iron-rich, but less alpha-enhanced than the
kinematically-smooth component of the inner halo. ECHOS are also chemically
distinct from other Milky Way components: more iron-poor than typical
thick-disk stars and both more iron-poor and alpha-enhanced than typical
thin-disk stars. In addition, the radial velocity dispersion distribution of
ECHOS extends beyond sigma ~ 20 km s^-1. Globular clusters are unlikely ECHOS
progenitors, as ECHOS have large velocity dispersions and are found in a region
of the Galaxy in which iron-rich globular clusters are very rare. Likewise, the
chemical composition of stars in ECHOS do not match predictions for stars
formed in the Milky Way and subsequently scattered into the inner halo. Dwarf
spheroidal (dSph) galaxies are possible ECHOS progenitors, and if ECHOS are
formed through the tidal disruption of one or more dSph galaxies, the typical
ECHOS [Fe/H] ~ -1.0 and radial velocity dispersion sigma ~ 20 km s^-1 implies a
dSph with M_tot >~ 10^9 M_Sun. Our observations confirm the predictions of
theoretical models of Milky Way halo formation that suggest that prominent
substructures are likely to be metal-rich, and our result implies that the most
likely metallicity for a recently accreted star currently in the inner halo is
[Fe/H] ~ -1.0.
