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We present high-precision radial velocity (RV) observations of Gaia BH1, thenearest known black hole (BH). The system contains a solar-type G star orbitinga massive dark companion, which could be either a single BH or an inner BH + BHbinary. A BH + BH binary is expected in some models where Gaia BH1 formed as ahierarchical triple, which are attractive because they avoid many of thedifficulties associated with forming the system through isolated binaryevolution. Our observations test the inner binary scenario. We have measured115 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 andare concentrated near a periastron passage, when perturbations due to an innerbinary would be largest. The RVs are well-fit by a Keplerian two-body orbit andshow no convincing evidence of an inner binary. Using REBOUND simulations ofhierarchical triples with a range of inner periods, mass ratios,eccentricities, and orientations, we show that plausible inner binaries withperiods $P_{\text{inner}} \gtrsim 1.5$ days would have produced largerdeviations from a Keplerian orbit than observed. Binaries with$P_{\text{inner}} \lesssim 1.5$ days are consistent with the data, but thesewould merge within a Hubble time and would thus imply fine-tuning. We presentupdated parameters of Gaia BH1's orbit. The RVs yield a spectroscopic massfunction $f\left(M_{\text{BH}}\right)=3.9358 \pm 0.0002\,M_{\odot}$ - about$7000\sigma$ above the $\sim2.5\,M_{\odot}$ maximum neutron star mass.Including the inclination constraint from Gaia astrometry, this implies a BHmass of $M_{\text{BH}} = 9.27 \pm 0.10 ~ M_{\odot}$.

ESPRESSO observations of Gaia BH1: high-precision orbital constraints and no evidence for an inner binary