We present a parallax measurement for the very cool degenerate WD 0346+246, the serendipitous discovery of which was reported by Hambly et al. We find an absolute parallax of 36+/-5mas, yielding a distance estimate of 28+/-4pc. The resulting absolute visual magnitude of the object is MV=16.8+/-0.3, making it the second-lowest luminosity white dwarf currently known. We use the distance estimate and measured proper motion to show that the object has kinematics consistent with membership of the Galactic halo. WD 0346+246 is therefore by far the coolest and least luminous of only a handful of plausible halo white dwarf candidates. As such, the object has relevance to the ongoing debate concerning the results of microlensing experiments and the nature of any baryonic dark matter component to the Galactic halo residing in stellar remnants.