We study the temporal asymmetry of over 600 bursts from the BATSE 3B c
atalog, encompassing a 200-fold range in peak flux. By comparing the r
ates of rise and fall of the flux near the highest peak of each burst,
we find that about two-thirds of the bursts exhibit a preferred asymm
etry in the sense that the flux rises more rapidly than it falls, conf
irming the conclusions of previous studies employing smaller databases
. The probability that the observed time asymmetry is a statistical fl
uctuation is less than 10(-5); therefore, models that predict time sym
metry of the burst profile are ruled out. We find no statistically sig
nificant correlation between burst temporal asymmetry and peak flux. T
his result is consistent with both cosmological and local interpretati
ons of the gamma-ray burst phenomenon.