  We calculate the {\it afterglow} emission for Gamma-Ray Bursts (GRBs) going
off in an extremely low density medium, referred to as {\it naked bursts}. Our
results also apply to the case where the external medium density falls off
sharply at some distance from the burst. The observed afterglow flux in this
case originates at high latitudes, i.e. where the angle between the fluid
velocity and the observer line of sight is greater than $\Gamma^{-1}$. The
observed peak frequency of the spectrum for naked bursts decreases with
observer time as $t^{-1}$, and the flux at the peak of the spectrum falls off
as $t^{-2}$. The 2--10 keV $X$-ray flux from a naked burst of average fluence
should be observable by the SWIFT satellite for time duration of about $10^3$
longer than the burst variability timescale. The high latitude emission
contributes to the early $X$-ray afterglow flux for any GRB, not just naked
bursts, and can be separated from the shocked inter-stellar medium (ISM)
emission by their different spectral and temporal properties. Measurements of
the high latitude emission could be used to map the angular structure of GRB
producing shells.
