  We develop a robust technique to determine the minimum variability timescale
for Gamma-ray Burst light curves, utilizing Haar wavelets. Our approach
averages over the data for a given GRB, providing an aggregate measure of
signal variation while also retaining sensitivity to narrow pulses within
complicated time-series. In contrast to previous studies using wavelets, which
simply define the minimum timescale in reference to the measurement noise
floor, our approach identifies the signature of temporally-smooth features in
the wavelet scaleogram and then additionally identifies a break in the
scaleogram on longer timescales as signature of a true, temporally-unsmooth
light curve feature or features. We apply our technique to the large sample of
Swift GRB Gamma-ray light curves and for the first time -- due to the presence
of a large number of GRBs with measured redshift -- determine the distribution
of minimum variability timescales in the source frame. We find a median minimum
timescale for long-duration GRBs in the source frame of $\Delta t_{\rm
min}=0.5$ s, with the shortest timescale found being on the order of 10 ms.
This short timescale suggests a compact central engine ($3 \times 10^3$ km). We
discuss further implications for the GRB fireball model and present a
tantalizing correlation between minimum timescale and redshift, which may in
part be due to cosmological time-dilation.
