  Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev
(SYK) model, $N$ Majorana fermions in $0+1$ dimensions with infinite-range
two-body interactions, which is attracting a lot of interest as a toy model for
holography. Here we show analytically and numerically that a generalized SYK
model with an additional one-body infinite-range random interaction, which is a
relevant perturbation in the infrared, is still quantum chaotic and retains
most of its holographic features for a fixed value of the perturbation and
sufficiently high temperature. However a chaotic-integrable transition,
characterized by the vanishing of the Lyapunov exponent and spectral
correlations given by Poisson statistics, occurs at a temperature that depends
on the strength of the perturbation. We speculate about the gravity dual of
this transition.
