  We show that a quantum dynamical localization effect can be observed in a
generic thermalization process of two weakly-coupled chaotic subsystems.
Specifically, our model consists of the minimal experimentally relevant
subsystems that exhibit chaos, which are 3-site Bose-Hubbard units. Due to the
high dimensionality of the composite 6-site system, the quantum localization
effect is weak and can not be resolved merely by the breakdown of
quantum-to-classical correspondence. Instead, we adopt an intrinsic definition
of localization as the memory of initial conditions, that is not related to the
underlying classical dynamics. We discuss the dynamics in the chaotic sea, and
in the vicinity of the mobility edge, beyond which ergodization is suppressed.
