He can't get promoted, he is the highest enlisted rank.
He technically could, if he was willing to take the officer's test and enroll in officer's training.
Enlisted men have been promoted to officer ranks even in the real world (and it tends to be a lot easier to do during wartime, as people above you in rank get killed off faster).
Considering the extreme nature of his service, the naval command could also theoretically waive other requirements and jump him up even higher in rank as a reward for pretty much saving the entire human race multiple times over.
The thing is, it won't happen. Because they want to keep him on the battlefield so they won't want to promote him, he would never feel comfortable anywhere other than the battlefield so he'll never ask for promotion, and 343 will never do it because then he'd stop being the Master Chief.
--- "Wall of Text'D!" --- oldskoolplayr76 "POwned again." --- blight family