Although the time profiles of gamma-ray bursts (GRBs) show extremely d
iverse behavior, their average statistical properties such as the aver
age peak-aligned profile and the autocorrelation function show simple
stretched exponential behavior. This could indicate that the diversity
of all bursts is just due to different random realizations of the sam
e simple stochastic process where the process is scale invariant in ti
me. We illustrate how both the diversity of GRB time profiles and some
important average statistical properties can be reproduced in this wa
y using a simple toy model for a stochastic pulse avalanche, which beh
aves as a chain reaction in a near-critical regime. We suggest that on
e possibility for the underlying physical process for generating GRBs
could be a ''chain detonation'' in which reconnecting magnetic turbule
nt features trigger each other.