Prominences can be unstable to a gravitational ballooning instability
of the Rayleigh-Taylor type. A two-dimensional generalized Kippenhahn-
Schluter prominence equilibrium is constructed. Its stability to ideal
, three-dimensional, short-wavelength line-tied perturbations is analy
zed. The instability requires a critical vertical density gradient. Fo
r a given magnetic field strength, the instability is sensitive to the
angle at which the magnetic field lines cross the prominence. An appr
oximate, sufficient, threshold condition is consistent with typical pr
ominence parameters.