  The nature of Gamma Ray Bursts (GRBs) remains a complete mystery, despite the
recent breakthrough discovery of low energy counterparts, although it is now
generally believed that at least most GRBs are at cosmological distances.
Virtually all proposed cosmological models require bursters to reside in
ordinary galaxies. This can be tested by looking inside the smallest GRB error
boxes to see if ordinary galaxies appear at the expected brightness levels.
This letter reports on an analysis of the contents of 26 of the smallest
regions, many from the brightest bursts. These events will have $z < 0.4$ and
small uncertainties about luminosity functions, K corrections and galaxy
evolutions; whereas the recent events with optical transients are much fainter
and hence have high redshifts and grave difficulties in interpretation. This
analysis strongly rejects the many models with peak luminosities of $10^{57}
photons \cdot s^{-1}$ as deduced from the $LogN-LogP$ curve with no evolution.
Indeed, the lower limit on acceptable luminosities is $6 \times 10^{58} photons
\cdot s^{-1}$. The only possible solution is to either place GRBs at
unexpectedly large distances (with $z > 5.9$ for the faint BATSE bursts) or to
require bursters to be far outside any normal host galaxy.
