Understanding the nature of the gamma-ray burst phenomenon is one of t
he outstanding problems of modern astrophysics, The identification of
counterparts at optical wavelengths is considered a crucial factor for
determining the origin of these events, Here we report the detection
and temporal properties of a variable optical source, which has been i
dentified(1,2) as the counterpart of the X-ray transient associated wi
th the gamma-ray burst GRB970508 (ref. 3). The initial optical images
were obtained only 5.8 hours after the initial gamma-ray burst, after
which the optical source was observed to brighten over the next two da
ys before declining in luminosity with a t(-1) power law, The decline
in brightness follows a form predicted by many relativistic fireball m
odels(4-7) for gamma-ray bursts, although the initial rise does not ap
pear to be compatible with the simplest of these models, The observed
fluence of the source at visible wavelengths over the period spanned b
y our observations is greater than or equal to 4.6 x 10(-8) erg cm(-2)
, about 3% of the fluence of the gamma-ray burst itself.