Actually, it ought to correspond to senior
chief. Which would be nicely consistent with what he says about his rank in "Playing God".
Namely, in the USN system, those three chevrons would mean that he has collected all the Petty Officer ranks (or ratings), but his next step would be to gain a "rocker" to indicate the first Chief Petty Officer rank. That is, he would move from >>> to (>>> at that point. And two little dots (stars in USN) atop that would mean the third Chief Petty Officer rank, Master CPO.
But the thing is, Starfleet doesn't use rockers. So >>> is Petty Officer 1st Class, but >>>. is CPO, >>>: is Senior CPO, and >>>:. is Master CPO.