  The possibility of observing many body localization of ultracold atoms in a
one dimensional optical lattice is discussed for random interactions. In the
non-interacting limit, such a system reduces to single-particle physics in the
absence of disorder, i.e. to extended states. In effect the observed
localization is inherently due to interactions and is thus a genuine many-body
effect. In the system studied, many-body localization manifests itself in a
lack of thermalization visible in temporal propagation of a specially prepared
initial state, in transport properties, in the logarithmic growth of
entanglement entropy as well as in statistical properties of energy levels.
