Under 141 (Pilot Schools) they require a Chief Instructor and, if needed, an Assistant Chief Instructor, amongst other official titled positions (Check Instructors, etc), requiring a close relationship with the local FSDO.
You'll never find anyting requiring a "Chief Instructor" or any other title under 61. Mostly sounds like a guy at the "flying club" who's been there a bit longer than the other instructors who takes care of some administrative desk work. Sounds like he/she has a little more experience and/or advanced ratings on his/her CFI than you. Other than, you're equals.