  We show that the expansion of an initially confined interacting 1D
Bose-Einstein condensate can exhibit Anderson localization in a weak random
potential with correlation length \sigma_R. For speckle potentials the Fourier
transform of the correlation function vanishes for momenta k > 2/\sigma_R so
that the Lyapunov exponent vanishes in the Born approximation for k >
1/\sigma_R. Then, for the initial healing length of the condensate \xi >
\sigma_R the localization is exponential, and for \xi < \sigma_R it changes to
algebraic.
