ABSTRACT We present a detailed spectral analysis of XMM-Newton and NuSTAR observations of the accreting transient black hole GRS 1739−278 during a very faint low hard state at ∼0.02% of the Eddington luminosity (for a distance of 8.5 kpc and a mass of 10 ). The broadband X-ray spectrum between 0.5 and 60 keV can be well-described by a power-law continuum with an exponential cutoff. The continuum is unusually hard for such a low luminosity, with a photon index of Γ = 1.39 ± 0.04. We find evidence for an additional reflection component from an optically thick accretion disk at the 98% likelihood level. The reflection fraction is low, with . In combination with measurements of the spin and inclination parameters made with NuSTAR during a brighter hard state by Miller et al., we seek to constrain the accretion disk geometry. Depending on the assumed emissivity profile of the accretion disk, we find a truncation radius of 15–35 (5–12 ) at the 90% confidence limit. These values depend strongly on the assumptions and we discuss possible systematic uncertainties.