  We suggest a quantum generalization of Chirikov's criterion for the onset of
chaos, i.e. the criterion of overlapping resonances. We illustrate our findings
using two one-dimensional hard-core particles in a box, with a small mass
defect as a perturbation over an integrable system, the latter represented by
two equal mass particles. Classical nonlinear resonances translate almost
verbatim to the quantum language. Quantum mechanics intervenes at a later
stage: the resonances occupying less one Hamiltonian eigenstate are excluded
from the chaos criterion. Resonances appear as contiguous patches of low purity
unperturbed eigenstates, separated by the groups of undestroyed states -- the
quantum analogues of the classical KAM tori.
