  If gamma-ray bursters are at cosmological distances - as suggested by their
isotropic distribution on the sky and by their number-intensity relation - then
the burst profiles will be stretched in time, by an amount proportional to the
redshift, 1 + $z$. We have tested data from the {\it Compton} Gamma Ray
Observatory's Burst and Transient Source Experiment (BATSE) for such time
dilation. Our measures of time scale are constructed to avoid selection effects
arising from intensity differences by rescale all bursts to fiducial levels of
peak intensity and noise bias. The three tests involved total count rate above
background, wavelet decomposition, and alignment of the highest peaks. In all
three tests, the dim bursts are stretched by a factor of about two relative to
the bright ones, over seven octaves of time scale. We calibrated the
measurements by dilating synthetic bursts that approximate the temporal
characteristics of bright BATSE bursts. Results are consistent with bursts of
BATSE's peak-flux completeness limit being at cosmological distances
corresponding to $z \sim 1$, and thus with independent cosmological
interpretations of the BATSE number-intensity relation.
