"Chief" O'Brien, as Chris SI said, originally came from him being the Transporter Chief, not any sort of rank. I remember him, through most of TNG, wearing Lieutenant's pips, not Ensign as that picture shows, though. (Aside from his first couple of appearances, most notably in "Encounter at Farpoint," where he was wearing Ensign pips
and command red.
) At any rate, the sense I got from TNG was definitely that he was an officer--he was tactical
officer, remember, on the
Rutledge. (Although of course we can argue the semantics of that one all day...
) It was when they moved him to DS9 that they decided to make "Chief" a rank, although it's unclear what exactly the full rank was--"Senior Chief Specialist" was used in dialogue once, but then the producers decided they didn't like it after all.
That said, I do kind of like the concept of Starfleet having enlisted personnel as well--if there's as many starships and starbases as DS9 and TNG respectively seemed to imply, there's no way they're going to be able to process every person on every one of them through four years at one facility on Earth...