It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional
XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we
show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the
spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for
the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and
the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization
hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not
separated by symmetry sectors.