A section chief was the leader of a section on Starfleet starships.
In 2266, the "good" half of Captain James T. Kirk ordered section chiefs on the USS Enterprise to assign personnel to the search for his "evil" half, and to report to Mr. Spock. (TOS: "The Enemy Within")
In 2369, a crewmember of USS Enterprise-D announced that all science personnel were to check in with their section chiefs to learn what their duties would be on the Remmler Array for the duration of a baryon sweep of the Enterprise. (TNG: "Starship Mine")