Chaffetz was a relentless and highly critical investigator of Hillary Clinton.
Democrats, joined by ethics lawyers from the George W. Bush and Barack Obama administrations, have said Trump's multinational businesses could pose major conflicts of interests if he doesn't divest himself and put those assets in a blind trust.
The president-elect said in tweets this week that he would leave his "great business in total" to focus on running the country and that legal documents are being drafted to "take me completely out of the business operations.
"The Presidency is a far more important task!" he tweeted.
It was unclear how Trump would accomplish removing himself, and he didn't elaborate. Critics have questioned whether leaving the businesses operations to his children — who are part of his transition team — would resolve any potential conflicts.
Rep. Elijah Cummings, the top Democrat on the Oversight Committee, sent a letter to Chaffetz shortly after the election urging a probe into Trump's potential conflicts and followed up this week with another letter signed by all 16 of his party colleagues on the panel.
"At the same time, during this two-week period, troubling new revelations about Mr. Trump's actions — as well as those of his family members and business associates — have made the need for robust congressional oversight even more urgent," the letter said.
Chaffetz said Thursday that it's only fair to give Trump some "leeway" during the transition from candidate to president.
"It's almost silly to suggest the investigation should begin now when he hasn't even been sworn in," Chaffetz said. "I didn't start an investigation of Hillary Clinton before she was sworn in [as secretary of state]; it was when the inspector general found potential wrongdoing that we started to look into it."
Cummings responded to Chaffetz's comments, noting that political party shouldn't provide cover for anyone, and there's no reason to wait.
"For Republicans, there was no allegation too small to investigate with respect to Secretary Clinton, but now there is no scandal too big to ignore for Donald Trump," the Maryland Democrat said in a statement. "Burying your head in the sand is the opposite of robust oversight, and it diminishes the integrity of the committee and the Congress. Donald Trump's global entanglements are unprecedented, and the committee would be doing him a service by addressing these conflicts of interest now instead of waiting until after he is sworn in as president."
Chaffetz said he's sure at some point he would be a thorn in the Trump administration's side.
"There will come a point when the Oversight Committee will be probing some things I'm sure the executive branch will not want us to be looking at," Chaffetz said. "It's happened for 200 years, and it will happen in the Trump administration as well."