By "1st enterprise" do you mean Kirk's (the 1st created by the franchise) or Archer's (the 1st built in the star trek universe)? Kirk's Enterprise had no character that served as Security Chief. The security personnel, known as "redshirts" by their uniform color, were highly expendable. Lt Commander Giotto was mentioned & seen as security chief during the episode Devil in the Dark. Lieutenant Freeman was security chief at some point, in "The Savage Curtain" we've seen Lt. Dickerson as Chief of Security & then Pavel Chekov during Star Trek: The Motion Picture. At last his task has been more than official in "Star Trek VI"
In "Mirror, Mirror", Sulu was referenced as being the head of security within the mirror universe.
On Archer's enterprise, Malcolm Reed served as security chief.