A chief is a leader, often of a tribe or clan. Native American tribes are headed by chiefs, and sometimes we call the president our "commander in chief."
A chief is the head honcho, the big kahuna, the top dog. Tribes are lead by chiefs, but so are firefighters (fire chief), policeman (police chief), and companies (Chief Executive Officer or CEO). When used as an adjective, chief describes the most important element or main ingredient of something. You couldn't make mac and cheese without the chief ingredients: macaroni and cheese.