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 \sim 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 ] \sim - 1.0 and radial velocity dispersion \sigma \sim 20 km s ^ { -1 } implies a dSph with M _ { \mathrm { tot } } \gtrsim 10 ^ { 9 } ~ { } M _ { \odot } . 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 ] \sim - 1.0 .