Title: Formation of a $33\,M_{\odot}$ black hole in a low-metallicity binary

Abstract: 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 ($\rm [M/H]=-2.2$) and is kinematically part of the Galactic halo, suggesting that the BH formed from a low-metallicity massive star. I show that orbits similar to that of Gaia BH3 are naturally produced through isolated binary evolution. The system's period and eccentricity can result from a broad range of initial orbits with a modest natal kick ($v_{\rm kick}\lesssim 75\,\rm km\,s^{-1}$) to the BH. I construct MESA 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. Stars of this size would fit inside most plausible pre-supernova orbits for the system without overflowing their Roche lobes. In addition, models with moderately rapid initial rotation ($\Omega/\Omega_{\rm crit} \gtrsim 0.45$) undergo chemically homogeneous evolution and never expand to radii larger than $10\,R_{\odot}$. There are thus multiple channels through which a low-metallicity, extreme-mass ratio binary could produce a system like Gaia BH3. Dynamical formation scenarios are also viable, and there is little doubt that both isolated and dynamically-formed BH binaries with orbits similar to Gaia BH3 will be discovered in Gaia DR4. 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.