  The oldest stars in the Milky Way (MW) bear imprints of the Galaxy's early
assembly history. We use FIRE cosmological zoom-in simulations of three MW-mass
disk galaxies to study the spatial distribution, chemistry, and kinematics of
the oldest surviving stars ($z_{\rm form} \gtrsim 5$) in MW-like galaxies. We
predict the oldest stars to be less centrally concentrated at $z=0$ than stars
formed at later times as a result of two processes. First, the majority of the
oldest stars are not formed $\textit{in situ}$ but are accreted during
hierarchical assembly. These $\textit{ex situ}$ stars are deposited on
dispersion-supported, halo-like orbits but dominate over old stars formed
$\textit{in situ}$ in the solar neighborhood, and in some simulations, even in
the galactic center. Secondly, old stars formed $\textit{in situ}$ are driven
outwards by bursty star formation and energetic feedback processes that create
a time-varying gravitational potential at $z\gtrsim 2$, similar to the process
that creates dark matter cores and expands stellar orbits in bursty dwarf
galaxies. The total fraction of stars that are ancient is more than an order of
magnitude higher for sight lines $\textit{away}$ from the bulge and inner halo
than for inward-looking sight lines. Although the task of identifying specific
stars as ancient remains challenging, we anticipate that million-star spectral
surveys and photometric surveys targeting metal-poor stars already include
hundreds of stars formed before $z=5$. We predict most of these targets to have
higher metallicity ($-3 < \rm [Fe/H] < -2$) than the most extreme metal-poor
stars.
