  We have studied the effects of a disordered optical potential on the
transport and phase coherence of a Bose-Einstein condensate (BEC) of 7Li atoms.
At moderate disorder strengths (V_D), we observe inhibited transport and
damping of dipole excitations, while in time-of-flight images, random but
reproducible interference patterns are observed. In-situ images reveal that the
appearance of interference is correlated with density modulation, without
complete fragmentation. At higher V_D, the interference contrast diminishes as
the BEC fragments into multiple pieces with little phase coherence.
