  A bound state in the continuum (BIC) is a spatially bounded energy eigenstate
lying in a continuous spectrum of extended eigenstates. While various types of
single-particle BICs have been found in the literature, whether or not BICs can
exist in genuinely many-body systems remains inconclusive. Here, we provide
numerical and analytical pieces of evidence for the existence of many-body BICs
in a one-dimensional Bose-Hubbard chain with an attractive impurity potential,
which was previously known to host a BIC in the two-particle sector. We also
demonstrate that the many-body BICs prevent the system from thermalization when
one starts from simple initial states that can be prepared experimentally.
