  We show that the onset of quantum chaos at infinite temperature in two
many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and
Anderson models, is characterized by universal behavior. Specifically, we show
that the onset of quantum chaos is marked by maxima of the typical fidelity
susceptibilities that scale with the square of the inverse average level
spacing, saturating their upper bound, and that the strength of the
integrability- or localization-breaking perturbation at these maxima decreases
with increasing system size. We also show that the spectral function below the
``Thouless'' energy (in the quantum-chaotic regime) diverges when approaching
those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily
small integrability- or localization-breaking perturbations result in quantum
chaos in the many-body quantum systems studied here.
