Generic perturbations of an integrable system lead to chaos. How they lead to chaos in the classical setting has been understood for decades and is captured by the Kolmogorov-Arnold-Moser theorem. No such result exists for quantum systems; moreover, the scaling of the threshold to chaos with system size is not well understood even classically. We propose some answers to these questions for quantum many-body systems, arguing that the onset of chaos can be understood as a Fock-space delocalization process. We also discuss incomplete thermalization when integrability is broken by an external trapping potential, which is relevant to "quantum Newton's cradle" experiments on ultracold atoms.