  A simple test for time-asymmetry is devised and carried out on the brightest
gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE)
on board the {\it Compton} Gamma Ray Observatory. We show evidence that
individual bursts are time-asymmetric on all time scales tested, from a time
scale shorter than that of pulses which compose GRBs to a time scale similar to
a greater envelope that contains these pulses. We also find bursts which
manifest significant asymmetry only on time scales comparable to the duration
of burst, and bursts for which no clear asymmetry on any time scale is present.
The sense of the asymmetry is that bursts and/or component structures rise in a
shorter time than they decay. We also find that our whole sample of bursts
taken together is time- asymmetric, in that there are significantly more bursts
and pulses where the rise is more rapid than the decay, on all time scales
tested and for all energy bands tested. When our whole GRB sample is binned at
64-ms and integrated over all BATSE energies, the statistical significance is
at the 6 $\sigma$ level. Models that predict time-symmetry are therefore
excluded.
