Using astrometric VLBI observations , we have determined the parallax of the black hole X-ray binary V404 Cyg to be 0.418 \pm 0.024 mas , corresponding to a distance of 2.39 \pm 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 < 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 .