  Cosmic balloons, consisting of relativistic particles trapped inside a
spherical domain wall, may be created in the early universe. We calculate the
balloon mass $M$ as a function of the radius $R$ and the energy density
profile, $\rho (r)$, including the effects of gravity. At the maximum balloon
mass $2GM/R\approx 0.52$ for any value of the mass density of the wall.
