  We have detected the intrinsic size of Sagittarius A*, the Galactic Center
radio source associated with a supermassive black hole, showing that the
short-wavelength radio emission arises from very near the event horizon of the
black hole. Radio observations with the Very Long Baseline Array show that the
source has a size of $24 \pm 2$ Schwarzschild radii at 7 mm wavelength. In one
of eight 7-mm epochs we also detect an increase in the intrinsic size of
$60^{+25}_{-17}$%. These observations place a lower limit to the mass density
of Sgr A* of $1.4\times10^{4}$ solar masses per cubic astronomical unit.
