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We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its non-equilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. As hallmarks of the many-body localized phase we confirm, furthermore, a logarithmic increase of the entanglement entropy in time and Poissonian leveldoi:10.1103/physrevlett.113.217201 pmid:25479517 fatcat:ycfpomo33nft3ixeh7tqecuvjm