The crossword solution for the term 'headwear for a building chief' is 'SUPERVISOR, ' which is a 10-letter word. A SUPERVISOR is a person who oversees and directs the work of other employees in an organization. Supervisors are responsible for ensuring that tasks are completed on time and to the required standards. They also provide guidance and support to their staff, and may be involved in hiring and firing decisions. In the context of a building chief, a SUPERVISOR would be responsible for overseeing the day-to-day operations of the building, such as maintenance, security, and customer service.