This paper explores the phenomenon of eigenstate thermalization in quantum systems. It shows that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions that form that state obey Berry's conjecture. Berry's conjecture, which is expected to hold only if the corresponding classical system is chaotic, states that the energy eigenfunctions behave as if they were Gaussian random variables. The paper reviews existing evidence and shows that previously neglected effects substantially strengthen the case for Berry's conjecture. It studies a rarefied hard-sphere gas as an example of a many-body system that is classically chaotic, and shows that an energy eigenstate obeying Berry's conjecture predicts a Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac distribution for the momentum of each particle, depending on the symmetry of the wave functions. The paper argues that these results constitute a new foundation for quantum statistical mechanics. It shows that a generic initial state will approach thermal equilibrium at least as fast as O(ħ/Δ)t⁻¹, where Δ is the uncertainty in the total energy of the gas. This result holds for an individual initial state, and no averaging over an ensemble of initial states is needed. The paper concludes that these results provide a new foundation for quantum statistical mechanics.This paper explores the phenomenon of eigenstate thermalization in quantum systems. It shows that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions that form that state obey Berry's conjecture. Berry's conjecture, which is expected to hold only if the corresponding classical system is chaotic, states that the energy eigenfunctions behave as if they were Gaussian random variables. The paper reviews existing evidence and shows that previously neglected effects substantially strengthen the case for Berry's conjecture. It studies a rarefied hard-sphere gas as an example of a many-body system that is classically chaotic, and shows that an energy eigenstate obeying Berry's conjecture predicts a Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac distribution for the momentum of each particle, depending on the symmetry of the wave functions. The paper argues that these results constitute a new foundation for quantum statistical mechanics. It shows that a generic initial state will approach thermal equilibrium at least as fast as O(ħ/Δ)t⁻¹, where Δ is the uncertainty in the total energy of the gas. This result holds for an individual initial state, and no averaging over an ensemble of initial states is needed. The paper concludes that these results provide a new foundation for quantum statistical mechanics.