Chaffetz, the Utah Republican who chairs the House Oversight and Government Reform Committee, is taking on his party's current No. 2 -- Kevin McCarthy
Chaffetz officially announced his bid for speaker on "Fox News Sunday," saying that McCarthy is a "good man" who has a "math problem" driven by conservatives' discontent, and that he's being recruited to enter the race.
He said with Boehner's retirement coming amid growing discontent from the party's right wing, Republicans shouldn't promote a member of his leadership team.
"You don't just give automatic promotion to the existing leadership team," he said. "That doesn't signal change. I think they want a fresh face and a fresh, new person who's actually there at the leadership table in the speaker's role."
Chaffetz said McCarthy has the support of the majority of the Republican conference, but will struggle to get 218 votes for his speakership on the House floor from the 246 House Republicans, largely because about 50 conservatives would vote against him.
"We were entrusted by the American people with the largest majority Republicans have ever had since Babe Ruth was swinging the baseball bat, but they didn't send us here to perpetuate the status quo," Chaffetz said Sunday.
"They want us to take that fight to the Senate," he said, alluding to the GOP-led chamber. "They want us to take that fight to the president."
Chaffetz is two years younger and has served less time in the House than the 50-year-old McCarthy, who has also faced questions about his lack of experience compared to other speakers.
His foray into the speaker's race comes days after McCarthy triggered controversy by pointing to the House committee investigating the Benghazi incident and crediting that panel's work with dragging down Hillary Clinton's poll numbers. He was repudiated by members of his own party, including Chaffetz, for politicizing the investigation.
"I am running for speaker of the House of Representatives because I want to lead the way on tackling the toughest issues facing the United States of America," said Chaffetz in the statement issued Sunday.
"The American people have entrusted Republicans with the largest majority since the 1920's, but with that majority comes a responsibility to get the job done that we were elected to do," he said. "I came to Congress to help fix problems, and as speaker I will fight every day to make that happen. I look forward to sharing my vision for the speakership with my colleagues and the American people."
Chaffetz's announcement that he's jumping into the speaker's race could open the door for other challengers, a source familiar with the House Republican leadership race said. Some names to watch closely include Reps. Jim Jordan and Jeb Hensarling.
Also worth keeping an eye on: Rep. Tom Price. Price is currently running for majority leader, but could jump into the speaker's race if he thinks he'll find more support there than in his current race against Rep. Steve Scalise, the source said.