A simple test for time asymmetry is devised and carried out on the bri
ghtest gamma-ray bursts (GRBs) detected by the Burst and Transient Sou
rce Experiment (BATSE) on board the Compton Gamma Ray Observatory. We
show evidence that individual bursts are time-asymmetric on all timesc
ales tested, from a timescale shorter than that of pulses which compos
e GRBs to a timescale similar to a greater envelope that contains thes
e pulses. We also find bursts which manifest significant asymmetry onl
y on timescales comparable to the duration of burst, and bursts for wh
ich no clear asymmetry on any timescale is present. The sense of the a
symmetry is that bursts and/or component structures rise in a shorter
time than they decay. We also find that our whole sample of bursts tak
en together is time-asymmetric, in that there are significantly more b
ursts and pulses where the rise is more rapid than the decay, on all t
imescales tested and for all energy bands tested. When our whole GRB s
ample is binned at 64 ms and integrated over all BATSE energies, the s
tatistical significance is at the 6 sigma level. Models that predict t
ime symmetry are therefore excluded.