It looks like the 2010 governor’s race in Ohio will pit two former U.S. House members against each other.

Republican John Kasich, a former chairman of the House Budget Committee, on Friday filed paperwork to begin raising money for an all-but-announced campaign against Democratic Gov. Ted Strickland, who’s seeking a second term that followed his own lengthy House tenure.

Kasich signed a “Designation of Treasurer” document from the Ohio Secretary of State’s office that establishes the campaign committee “Kasich for Ohio.”