  We have observed self-sustained radial oscillations in a large
magneto-optical trap (MOT), containing up to $10^{10}$ Rb$^{85}$ atoms. This
instability is due to the competition between the confining force of the MOT
and the repulsive interaction associated with multiple scattering of light
inside the cold atomic cloud. A simple analytical model allows us to formulate
a criterion for the instability threshold, in fair agreement with our
observations. This criterion shows that large numbers of trapped atoms $N>10^9$
are required to observe this unstable behavior.
