He wont' direct Star Trek 3 but Jon M. Chu's rising career is still a fascinating one to watch. From Step Up to Justin Bieber to G.I. Joe to horror. Seems like a natural progression to me. Chu is producing and developing a "high concept" horror story called Run for Lionsgate, according to Deadline.
No indication of whether he will direct as well as "godfather," but I can't imagine why he wouldn't. And if Lionsgate wants a franchise of the film that's described as an "action horror," Chu seems like the right guy to get in on the ground floor, both in terms of the energy on screen he brings to his action-driven films thus far, and beacause he's directed or will direct at least two installments of each of them (yes, Justin Bieber documentaries included).