The distance to the black hole binary GX339-4 remains a topic of debate. We examine high-resolution optical spectra of the NaD lines resolving the velocity structure along the line of sight. We find this to be complex, with at least nine components, mostly blue-shifted, spanning a velocity range of nearly 200km/s. The presence of components with a large blue-shift rules out a nearby location and requires that the binary be located at or beyond the tangent point, implying a lower limit to the distance of ~6kpc. The presence of a significant red-shifted component at +30km/s is even more intriguing as GX339-4 also has a slightly positive systemic velocity, suggesting that the source, and this cloud, could be on the far side of the Galaxy, where the radial velocities due to Galactic rotation become positive again. If this is the case, we require a distance of ~15kpc. This is less secure than the 6kpc lower limit however. We discuss the implications of these possible distances for the outburst and quiescent luminosities, and the nature of the companion star, and argue that a large distance is consistent with these characteristics. In particular, it would explain the non-detection of the companion star during the faintest states.

Accepted for publication in the Astrophysical Journal