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 Observatorys 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 BATSEs 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.
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