  We determine some basic properties of stars that produce spectacular
gamma-ray bursts at the end of their life. We assume that accretion of the
outer portion of the stellar core by a central black hole fuels the prompt
emission, and that fall-back and accretion of the stellar envelope later
produces the plateau in the X-ray light curve seen in some bursts. Using X-ray
data for three bursts we estimate the radius of the stellar core to be ~ 1-3 x
10^10 cm, and that of the stellar envelope to be ~ 1-2 x 10^11 cm. The density
profile in the envelope is fairly shallow, with \rho ~ r^-2. The rotation
speeds of the core and envelope are ~ 0.05 and ~ 0.2 of the local Keplerian
speed, respectively.
