Are Gamma-Ray Bursts at Cosmological Distances Optically-Thin?

The observed spatial distribution of $\gamma-$ray bursts indicates that they probably originate at cosmological distances. At this distance scale their variability timescale and flux above MeV imply an initial optical-depth to pair production $> 10^{10}$. This appears to be in conflict with their highly non-thermal spectra. We show that this difficulty can be removed if axion bursts from supernovae are converted to $\gamma-$rays over cosmological distances. Nonthermal bursts with the relevant flux, duration, variability and spectra are obtained just for the range of axion masses of $10^{-5}-10^{-4}{\rm eV}$ that accounts for the cold dark matter in the universe. The observed rate of $\gamma-$ray bursts implies that axions should be converted efficiently to photons in only one out of $\sim 10^{4}$ supernovae.