Chief: if you are talking about the leader of a Native American tribe, you use this word. It can also be used in job titles to describe the head of a company or organization. (Chief of Police, Fire Chief and Chief Executive Officer are the most common examples.) You CANNOT say "My chief. . . "
Chef: is a cook, usually one whose profession is cooking in a restaurant. You CANNOT say "My chef. . . "
Boss: someone who supervises workers in a company or organization. You CAN say "My boss. . ."