For now, we only know that Naruto thinks hes a chunnin, after all he let Ibiki imply he was so (or does my memory play tricks with me)
As for Naruto being promoted chunnin, we saw Tsunade checking everyones portfolio out, shes seen Naruto in action and thinks hes a future hokage, so any promotions to chunnin with her signature on are bound to include Naruto.