State Sen. Anthony Bouchard, a Republican, filed a statement of candidacy, according to Federal Election Commission records.
Cheney drew widespread criticism for voting with Democrats and nine other Republicans last week to impeach then-President Donald Trump.
“Wyoming was President Trump’s best state both times he ran. That’s because Wyoming voters are strong conservatives who want our leaders to stand up for America, defend our freedoms, fight for our way of life and always put working people first as President Trump did,” Bouchard said in a statement Wednesday.
“Liz Cheney’s long-time opposition to President Trump and her most recent vote for Impeachment shows just how out-of-touch she is with Wyoming. Wyoming taxpayers need a voice in Congress who will stand up to Nancy Pelosi and the Democrats, and not give them cover. That’s why I’m running for Congress,” he added.
Bouchard is in his second term after entering office in 2017.
Cheney’s office didn’t respond to a request for comment.
The congresswoman has defended her impeachment vote, saying she felt Trump deserved to be impeached because he allegedly “lit the flame” of the Jan. 6 U.S. Capitol breach.
“None of this would have happened without the President. The President could have immediately and forcefully intervened to stop the violence. He did not. There has never been a greater betrayal by a President of the United States of his office and his oath to the Constitution,” she wrote in a statement.
Cheney’s words were repeatedly referenced by Democrats on and off the House floor when debating the impeachment resolution. She is the No. 3 Republican in the House.
Colleagues are attempting to remove her from the House leadership team and the Wyoming Republican Party said there was a “clear” consensus from voters that Cheney’s vote was wrong.
“We are receiving the message loud and clear that what happened yesterday is a true travesty for Wyoming and the country,” the party said in a Jan. 13 statement, noting its telephone hadn’t stopped ringing.
A petition for Cheney’s removal has topped 36,000 votes as of Jan. 20.