  We have measured the T90 and T50 durations of bright and dim gamma-ray bursts
(GRBs) detected by the Compton Gamma Ray Observatory's Burst and Transient
Source Experiment (BATSE). The T90 (T50) duration is defined as the interval
over which 5\% (25\%) to 95\% (75\%) of the burst counts accumulate. Out of 775
bursts observed by BATSE, 159 bursts were analyzed; bursts with durations
shorter than 1.5 s were excluded. A Kolmogorov-Smirnov test yields a
probability of 6 x $10^{-5}$ that the T50 durations of the dim and bright
samples are drawn from the same parent population. We find that the centroid
and extent of the duration distribution for the dim sample are scaled by
approximately a factor of two relative to those of the bright sample. The
measured time dilation factor is not sensitive to choice of energy band. These
results are quantitatively consistent with previous tests for time dilation in
a smaller sample of BATSE bursts. The dimmer bursts, if cosmological, would lie
at redshifts of order two.
