The recently discovered binary LB-1 has been reported to contain a ∼ 70 M black hole (BH). The evidence for the unprecedentedly high mass of the unseen companion comes from reported radial velocity (RV) variability of the Hα emission line, which has been proposed to originate from an accretion disk around a BH. We show that there is in fact no evidence for RV variability of the Hα emission line, and that its apparent shifts instead originate from shifts in the luminous star's Hα absorption line. If not accounted for, such shifts will cause a stationary emission line to appear to shift in anti-phase with the luminous star. We show that once the template spectrum of a B star is subtracted from the observed Keck/HIRES spectra of LB-1, evidence for RV variability vanishes. Indeed, the data rule out periodic variability of the line with velocity semi-amplitude K Hα > 1.3 km s −1 . This strongly suggests that the observed Hα emission does not originate primarily from an accretion disk around a BH, and thus that the mass ratio cannot be constrained from the relative velocity amplitudes of the emission and absorption lines. The nature of the unseen companion remains uncertain, but a "normal" stellar-mass BH with mass 5 M/M 20 seems most plausible. The Hα emission likely originates primarily from circumbinary material, not from either component of the binary.