I’m reading the “problematic rank history” subsection of Miles O’Brien Memory Alpha article, and oh boy what a journey!

Here is a summary of what it says and my personal conclusions based on inconstant on-screen dialog and visuals:

O’Brien is seen in a red and gold uniform. That uniform either has a single black pip, a single gold pip, or two gold pips. And he is referred to as Ensign, Lieutenant, (a) Chief ( of some capacity), Warrant Officer, or Ensign Junior Grade depending on the episode/script/book prior to him getting a proper noncom badge sometime during Deep Space Nine.

Timeline of events:

• Ensign Miles O’Brien served as officer on the Rutledge. He became the ships tactical officer and got his first gold uniform.

• Due to his service record, he was handpicked to be a bridge officer on the new Enterrpise-D. This put him on the command track and gave him a red uniform.

• O’Brien felt under-utilized on the bridge and since there were no openings for a tactical officer, he requested a transfer to operations. During this time he bounced around the ship as needed, spending most of his time in Main Engineering or a transporter room. He was promoted to the rank of full Lieutenant for his hard work.

• During this time, O’Brien briefly outranked Lieutenant Junior-Grade Worf. But due to them being in different departments, neither reported to each other except for when O’Brien had to defer to matters of ship’s security.

• Starfleet Command floated the idea of reintroducing non-commissioned officers into the ranks after having been phased out over the past few generations. They decided to testbed the idea with an officer aboard the Enterprise. O’Brien was approached and he accepted the “demotion” to Chief Petty Officer. Because this idea was only in testing at the time, he formally retained his rank of Lieutenant.

• When O’Brien transferred to Deep Space Nine, the NCO test was formalized and his rank was officially changed to Chief Petty Officer. At first, he was given a single, black pip which previously indicated someone was a Warrant Officer. The reasoning was that as an enlisted officer his rank was technically inferior to an Ensign. Ensigns fresh out of the Academy jokingly referred to noncom officers as “Ensign Junior-Grade.”

• Some time later, after non-commissioned officers became more ubiquitous in Starfleet (and probably after receiving multiple requests for more distinct rank insignia), Starfleet updated the noncom uniforms to display tiny badges with chevrons. These badges also display pips representing the equivalent rank were that enlisted person an officer. The badge worn by O’Brien displayed three chevrons (Chief Petty Officer) and two pips (Lieutenant, preserving his original commissioned rank).

That's because NCO stands for Newly Cloned O'Brien.