Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessary rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiments is proposed. Introduction.-It has been known for almost 60 years that non-interacting particles in one-dimensional disordered systems exhibit Anderson localization [1]. Transport in these systems is exponentially suppressed with the system size, and without coupling to the environment, these systems are non-ergodic at any temperature. Anderson localized systems are, however, non-generic, since they do not include interactions which allow for the exchange of energy. For many years it was assumed that interactions generally restore ergodicity and destroy localization [2]. A decade ago, using non-equilibrium diagrammatic techniques, it was argued that Anderson localization is stable under the addition of a small shortranged interactions [3], a phenomenon currently known as many-body localization (MBL). Many-body localized systems are the only known generic non-ergodic systems which do not follow the assumptions of statistical mechanics [4][5][6]. While the realization of MBL systems presents challenges in condensed matter systems due to inevitable presence of phonons [7,8], recent experiments in cold atoms have provided evidence of the existence of MBL in both one-dimensional [9-11] and two-dimensional systems [12].