  The Ca~II H \& K lines are among the few features available to infer the
metallicity of extremely metal-poor stars from medium-resolution spectroscopy.
Unfortunately, these lines can overlap with absorption produced in the
intervening interstellar medium, introducing systematic errors in the derived
metallicities. The strength of the Ca~II infrared triplet lines can also be
measured at extremely low metallicities, and it is not affected by interstellar
absorption, but suffers significant departures from Local Thermodynamical
Equilibrium (LTE). We investigate the feasibility of adopting the Ca~II
infrared triplet as a metallicity indicator in extremely metal-poor stars using
state-of-the art Non-LTE models including the most recent atomic data. We find
that the triplet lines exhibit Non-LTE abundance corrections that can exceed
0.5\,dex. When interstellar absorption affecting the Ca~II resonance lines is
accounted for using high-resolution observations, the agreement between Non-LTE
abundances for the triplet and those for the resonance lines, with only minor
departures from LTE, is excellent. Non-LTE effects strengthen the Ca~II IR
triplet lines, facilitating measurements at very low metallicities, compared
with LTE estimates, down to $\rm [Fe/H]=-6.0$. This result has important
implications for the discovery of primitive stars in our Galaxy and others,
since instruments are most sensitive at red/near-infrared wavelengths, and tens
of millions of spectra covering the Ca~II IR triplet will soon become available
from the Gaia, DESI, WEAVE, and PFS missions.
