  Over a decade ago it was established that the remarkable high energy
transients, known as soft gamma-ray repeaters (SGRs), are a Galactic population
and originate from neutron stars with intense (<~ 10^15 G) magnetic fields
("magnetars"). On 27 December 2004 a giant flare (fluence >~ 0.3 erg/cm^2) was
detected from SGR 1806-20. Here we report the discovery of a fading radio
counterpart. We began a monitoring program from 0.2GHz to 250GHz and obtained a
high resolution 21-cm radio spectrum which traces the intervening interstellar
neutral Hydrogen clouds. Analysis of the spectrum yields the first direct
distance measurement of SGR 1806-20. The source is located at a distance
greater than 6.4 kpc and we argue that it is nearer than 9.8 kpc. If true, our
distance estimate lowers the total energy of the explosion and relaxes the
demands on theoretical models. The energetics and the rapid decay of the radio
source are not compatible with the afterglow model that is usually invoked for
gamma-ray bursts. Instead we suggest that the rapidly decaying radio emission
arises from the debris ejected during the explosion.
