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Abstract We present high-precision radial velocity observations of Gaia BH1, the nearest known black hole (BH). The system contains a solar-type G star orbiting a massive dark companion, which could be either a single BH or an inner BH + BH binary. A BH + BH binary is expected in some models where Gaia BH1 formed as a hierarchical triple, which is attractive because they avoid many of the difficulties associated with forming the system through isolated binary evolution. Our observations test the inner binary scenario. We have measured 115 precise RVs of the G star, including 40 from ESPRESSO with a precision of 3–5 m s⁻¹, and 75 from other instruments with a typical precision of 30–100 m s⁻¹. Our observations span 2.33 orbits of the G star and are concentrated near a periastron passage, when perturbations due to an inner binary would be largest. The RVs are well-fit by a Keplerian two-body orbit and show no convincing evidence of an inner binary. UsingREBOUNDsimulations of hierarchical triples with a range of inner periods, mass ratios, eccentricities, and orientations, we show that plausible inner binaries with periodsP_inner≳ 1.5 days would have produced larger deviations from a Keplerian orbit than observed. Binaries withP_inner≲ 1.5 days are consistent with the data, but these would merge within a Hubble time and would thus imply fine-tuning. We present updated parameters of Gaia BH1's orbit. The RVs yield a spectroscopic mass function $f\left(M_{\mathrm{BH}}\right)=3.9358\pm 0.0002M_{\odot }$—about 7000σabove the ∼2.5M_⊙maximum neutron star mass. Including the inclination constraint from Gaia astrometry, this implies a BH mass ofM_BH= 9.27 ± 0.10M_⊙.