15 ILCS 505/4

If any person elected to the office of Treasurer shall fail to give bond or take the oath required of him, within ten days after he is declared elected, the office shall be deemed vacant, and if the Treasurer, being required to give additional bond, as provided in Section 3 hereof, fails to do so within twenty days after notice of such requirement, his office may, in the discretion of the Governor, be declared vacant, and filled as provided by law.