  We show that the condition for the appearance of quantum chaos (Wigner-Dyson
distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a
dilute gas of many hard spheres is $\lambda \ll \ell$, where $\lambda$ is the
wavelength of a typical particle and $\ell$ is the mean free path between
collisions. For fermions with Fermi wavelength $\lambda_F \ll \ell$, this
implies that all energy eigenstates, including the ground state, are chaotic.
Physical implications are discussed.
