  We constrain the minimum variability timescales for 938 GRBs observed by the
Fermi/GBM instrument prior to July 11, 2012. The tightest constraints on
progenitor radii derived from these timescales are obtained from light curves
in the hardest energy channel. In the softer bands -- or from measurements of
the same GRBs in the hard X-rays from Swift -- we show that variability
timescales tend to be a factor 2--3 longer. Applying a survival analysis to
account for detections and upper limits, we find median minimum timescale in
the rest frame for long-duration and short-duration GRBs of 45 ms and 10 ms,
respectively. Fewer than 10% of GRBs show evidence for variability on
timescales below 2 ms. These shortest timescales require Lorentz factors
$\gtrsim 400$ and imply typical emission radii $R \approx 1 {\times} 10^{14}$
cm for long-duration GRBs and $R \approx 3 {\times} 10^{13}$ cm for
short-duration GRBs. We discuss implications for the GRB fireball model and
investigate whether GRB minimum timescales evolve with cosmic time.
