Observations of the Perseus cluster by the HEAO 1 satellite have revealed a faint X-ray halo extending at least 2.5 deg from the center and contributing between 5% and 20% to the total luminosity. This may be of nonthermal origin, but it also may be explained in terms of hot gas bound by the gravitational field of the cluster. Statistical uncertainties made it impossible to detect any such halo in the Coma cluster. Observations of the Virgo cluster confirmed the detection by the Ariel 5 satellite of a broad region of faint X-ray emission (core radius 60 arcmin). If the very extended X-ray emission from Virgo is due to hot intracluster gas, the density of this gas is lower than expected from a consideration of gas and galaxy densities in the Perseus cluster.