  The Galactic stellar halo is predicted to have formed at least partially from
the tidal disruption of accreted dwarf galaxies. This assembly history should
be detectable in the orbital and chemical properties of stars. The H3 Survey is
obtaining spectra for 200,000 stars, and, when combined with Gaia data, is
providing detailed orbital and chemical properties of Galactic halo stars.
Unlike previous surveys of the halo, the H3 target selection is based solely on
magnitude and Gaia parallax; the survey therefore provides a nearly unbiased
view of the entire stellar halo at high latitudes. In this paper we present the
distribution of stellar metallicities as a function of Galactocentric distance
and orbital properties for a sample of 4232 kinematically-selected halo giants
to 100 kpc. The stellar halo is relatively metal-rich, [Fe/H]=-1.2, and there
is no discernable metallicity gradient over the range $6<R_{\rm gal}<100$ kpc.
However, the halo metallicity distribution is highly structured including
distinct metal-rich and metal-poor components at $R_{\rm gal}<10$ kpc and
$R_{\rm gal}>30$ kpc, respectively. Metal-poor stars with [Fe/H]$<-2$ are a
small population of the halo at all distances and orbital categories. We
associate the "in-situ" stellar halo with stars displaying thick-disk chemistry
on halo-like orbits; such stars are confined to $|z|<10$ kpc. The majority of
the stellar halo is resolved into discrete features in orbital-chemical space,
suggesting that the bulk of the stellar halo formed from the accretion and
tidal disruption of dwarf galaxies. (ABRIDGED)
