  A Bose-Einstein condensate in an external potential consisting of a
superposition of a harmonic and a random potential is considered theoretically.
  From a semi-quantitative analysis we find the size, shape and excitation
energy as a function of the disorder strength. For positive scattering length
and sufficiently strong disorder the condensate decays into fragments each of
the size of the Larkin length ${\cal L}$. This state is stable over a large
range of particle numbers. The frequency of the breathing mode scales as
$1/{\cal L}^2$. For negative scattering length a condensate of size ${\cal L}$
may exist as a metastable state. These finding are generalized to anisotropic
traps.
