Chair and one of directors insisted that my project is theirs... what should I do?
Please note before reading: The text below contains only my opinions. 

Accusing someone with stealing ideas is as ugly as stealing the idea itself.
As far as I understand, the department chair really liked the project and trying to get on the gravy train. Therefore, I do not believe trying to be reasonable with these kind of behavior will get you nowhere. Especially including faculty members, who have literally nothing to do with this matter is extremely rude and unprofessional.

If I were in your shoes, I would do follow these steps:


Explain the situation to the students working in the project (if any).
Ignore his mobbing (yes, I think this is heavy mobbing), and hand in nothing including surveys, project reports etc.
Write to IRB about this matter immideately and ask them for approval that the work was submitted by me.
Ask him to file a written complaint with the evidence that proves the idea belonged to him originally.
Collect/copy/back-up everything that proves the project proposal does not belong to the department chair.
Write to the dean (or whoever he is subordinate of) about this matter, asking to resolve this by official methods (as I have stated, this is clearly mobbing).


It is your own decision to leave the school. I would do the same, probably. But please keep in mind that these kind of issues can only be solved by legal process. All he can do is denounce you, and at this point, he will do it anyways if you drop the project.

Also, I believe that keeping your so called "ideas" to yourself is a responsibility. Either you immideately execute your ideas, or you accept the risk that someone can do it before you.
And there is nothing to do after that happens.