Former Wisconsin Governor Tommy Thompson on Monday said he would join the race for the Senate seat being vacated by Wisconsin Senator Herb Kohl.

“I filed my incorporation documents today which allows me to build my organization, raise money so I can go out there and tell the story,” Thompson said on WTMJ-AM 620 radio, the Chicago Tribune reported.

Thompson, who as a four-term governor carries high name recognition in Wisconsin, joins two announced candidates for the GOP nomination: former Rep. Mark Neumann and Wisconsin Assembly Speaker Jeff Fitzgerald.

Wisconsin Rep. Tammy Baldwin is the first and so far only Democrat to formally declare her candidacy for the seat.

The openly gay Baldwin is a perennial favorite in her district and has never lost a race. However, she remains untested in a statewide election. If elected, she would become the first openly gay U.S. senator.

Baldwin has already said her candidacy would not be about her sexual orientation.

“I have always since the beginning of all my adult life been out and honest about my sexual orientation, and I think that voters appreciate the values of honesty and expect integrity in their elected officials.”

The race, Baldwin added, “won't be about me.”

Thompson's record on gay rights includes him saying in 2008 that he believes businesses should have the right to fire gay employees. The next day during an appearance on HBO's Real Time with Bill Maher, he profusely denied he believes in discrimination in the workplace based on sexual orientation, explaining that he was not feeling well and did not answer the question correctly.