  The onset of thermalization in a closed finite system of randomly interacting
bosons, at the level of a single eigenstate, is discussed. The main interest is
in the emergence of the Bose-Einstein distribution of single-particle
occupation numbers, establishing a global and local criterion for
thermalization. We show how to define the temperature of a given eigenstate,
provided that it has a chaotic structure in the basis defined by
single-particle states. The analytical expression for the eigenstate
temperature as a function of the inter-particle interaction and energy is
complemented by numerical data.
