  A $33\,M_\odot$ black hole (BH) was recently discovered in an 11.6-year
binary only 590 pc from the Sun. The system, Gaia BH3, contains a
$0.8\,M_\odot$ low-metallicity giant ($\rm [M/H]=-2.2$) that is a member of the
ED-2 stellar stream. This paper investigates whether the system could have
formed via isolated binary evolution. I construct evolutionary models for
metal-poor massive stars with initial masses ranging from $35-55\,M_{\odot}$,
which reach maximum radii of $1150-1800\,R_{\odot}$ as red supergiants. I then
explore what combinations of initial orbit, mass loss, and natal kick can
produce the period and eccentricity of Gaia BH3. Initial orbits wide enough to
accommodate the BH progenitor as a red supergiant can match the observed period
and eccentricity, but only if the BH formed with a significant natal kick
($v_{\rm kick}\gtrsim 20\, {\rm km\,s^{-1}}$). These models are disfavored
because such a kick would have ejected the binary from the ED-2 progenitor
cluster. I conclude that Gaia BH3 likely formed through dynamical interactions,
unless the BH progenitor did not expand to become a red supergiant. Only about
1 in 10,000 stars in the solar neighborhood have metallicities as low as Gaia
BH3. This suggests that BH companions are dramatically over-represented at
low-metallicity, though caveats related to small number statistics apply. The
fact that the luminous star in Gaia BH3 has been a giant -- greatly boosting
its detectability -- only for $\sim$1% of the time since the system's formation
implies that additional massive BHs remain to be discovered with only
moderately fainter companions. Both isolated and dynamically-formed BH binaries
with orbits similar to Gaia BH3 are likely to be discovered in Gaia DR4.
