references issue

Very few companies allow their staff to give employment references. Employers worry about the legal consequences

Asking someone who has the same employer to give an employment reference would be considered inappropriate here. They should expect that person to discuss the matter with higher-ups.

correct

the chairperson could be fired for providing a reference - especially if it was not cleared

Chairman is the person who does the annual peer review of the employee. If the employer knows that the employee is persuing another job opportunities, is the confidentiality of the employee lost in that process put him at risk. Obviously an issues with the employee should have been brought to the division chairman. Does the employer has right to know that he is persuing other job opportunities? Does that not put the employee relation with employer at risk. Is employer (CEO) not supposed to let the chairman know any concerns he has about the employee in a timely manner as part of peer review or annual performance review. Reference is about the professional conduct and competence.

It would be best if the employee did not let the chairperson know they are pursuing other work.

The chairperson's responsibility and allegiance are to the employer first.

The chairperson is the employer in effect. It is a mistake to think otherwise.

He does not make my contract though. He does not know what is in my contract. How does he become part of administration?

As a chairperson, he is part of the management/administration of the university.

Again, his responsibility is to the university first. It would be inappropriate for him to give a reference without clearing it with the university.