Experiments with ultracold gases have made it possible to study dynamics of (nearly-) isolated quantum many body systems, which has revived theoretical interest on this topic. In generic isolated systems, one expects nonequilibrium dynamics to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. However, it is not obvious what feature of a many-body system makes quantum thermalization possible, in a sense analogous to that in which dynamical chaos makes classical thermalization possible. Underscoring that new rules could apply in the quantum case, experimental studies in one-dimensional systems have shown that traditional statistical mechanics can provide incorrect predictions for the outcomes of relaxation dynamics. We show that isolated "quantum-chaotic" systems do in fact relax to states in which observables are well-described by statistical mechanics. Moreover, we argue that the time evolution itself only plays an auxiliary role as thermalization occurs at the level of individual eigenstates.