  G\"odel universe, one of the most interesting exact solutions predicted by
General Relativity, describes a homogeneous rotating universe containing naked
closed time-like curves (CTCs). It was shown that such CTCs are the consequence
of the null energy condition in General Relativity. In this paper, we show that
the G\"odel-type metrics with chronology protection can emerge in
Einstein-Horndeski gravity. We construct such exact solutions also in
Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.
