  It is believed that thermalization in closed systems of interacting particles
can occur only when the eigenstates are fully delocalized and chaotic in the
preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate
that at variance with this common belief the typical situation in the systems
with two-body inter-particle interaction is much more complicated and allows to
treat as thermal even eigenstates that are not fully delocalized. Using a
semi-analytical approach we establish the conditions for the emergence of such
thermal states in a model of randomly interacting bosons. Our numerical data
show an excellent correspondence with the predicted properties of {\it
localized thermal eigenstates}.
