Using astrometric VLBI observations, we have determined the parallax of the
black hole X-ray binary V404 Cyg to be 0.418 +/- 0.024 milliarcseconds,
corresponding to a distance of 2.39 +/- 0.14 kpc, significantly lower than the
previously accepted value. This model-independent estimate is the most accurate
distance to a Galactic stellar-mass black hole measured to date. With this new
distance, we confirm that the source was not super-Eddington during its 1989
outburst. The fitted distance and proper motion imply that the black hole in
this system likely formed in a supernova, with the peculiar velocity being
consistent with a recoil (Blaauw) kick. The size of the quiescent jets inferred
to exist in this system is less than 1.4 AU at 22 GHz. Astrometric observations
of a larger sample of such systems would provide useful insights into the
formation and properties of accreting stellar-mass black holes.Comment: Accepted for publication in ApJ Letters. 6 pages, 2 figure