The gamma-ray diffuse emission has been recently observed with unprece
dented accuracy by the Compton Gamma Ray Observatory (CGRO) at photon
energies in the range between 100 MeV and 10 GeV. A residual isotropic
diffuse radiation is measured for the first time at low galactic lati
tude, with little variation over different portions of the sky. That m
easurement translates into a tight constraint on the abundance of diff
use gas in the dark matter halo surrounding our galaxy. If that halo c
ontained significant amounts of gas, cosmic-ray protons originating fr
om the galactic disc would interact with it, yielding a gamma-ray flux
which CGRO would have observed. By using a diffusion model which corr
ectly reproduces the radial distribution of cosmic-rays along the gala
ctic plane, we infer an upper limit of similar to 2 to 4% on the fract
ion of gas in diffuse form or in clouds. The flatter the halo, the str
onger the bound. That result only applies in the region where cosmic-r
ays are confined, i.e., for a galactocentric radius R < 20 kpc and a h
eight \z\ < 4 kpc. In particular, a thin disc is severely constrained
by the gamma-ray measurements.