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Over the course of the debate's 90 minutes, the Fox News anchor's questions on major policy issues and top news stories ellicited praise on social media.
Wallace rattled through questions on a range of issues from immigration to abortion to gun control, while touching of the top news events including Donald Trump's baseless claim that the general election is rigged against him.
He also did not tolerate interruptions, occasionally asking the crowd at the University of Las Vegas to stay quiet during the debate.
Reporters and viewers lauded Wallace's performance as soon as the debate concluded:
@rempower @OWNingLight thought #ChrisWallace did a good job.
- Oprah Winfrey (@Oprah) October 20, 2016
Chris Wallace is just amazing at this.
- Farhad Manjoo (@fmanjoo) October 20, 2016
Nice work, Chris Wallace!
- David Fahrenthold (@Fahrenthold) October 20, 2016
Chris Wallace a big winner from tonight https://t.co/FFXF1W64oP
- Rich Lowry (@RichLowry) October 20, 2016
Can we just elect Chris Wallace instead?
- Bret Stephens (@StephensWSJ) October 20, 2016
Chris Wallace nailed it.
- Kyle Blaine (@kyletblaine) October 20, 2016
Chris Wallace is the first Fox News anchor to moderate a presidential debate and hands down this year's best
- Jon Passantino (@passantino) October 20, 2016
Chris Wallace knocked it out of the park as moderator, I would say.
- Byron Tau (@ByronTau) October 20, 2016
The Fox News anchor's performance did not ellicit the anger some top Trump supporters reserved for previous moderators, including NBC's Lester Holt, CNN's Anderson Cooper, and ABC's Martha Raddatz.
The Trump campaign appeared pleased with Wallace's turn as a moderator.
"Chis Wallace did a good job on keeping them on the issues," former New York City Mayor and Trump advisor Rudy Giuliani told Sean Hannity after the debate.
Shortly after the moderators were announced earlier this year, Wallace garnered criticism when he said it was not his job to be a "truth squad."
"It's up to the other person to catch them on that," Wallace said. "I view it as kind of like being a referee in a heavyweight championship fight. If it succeeds, after it's over people will say, 'You did a great job. I don't even remember you being on the stage.'"
Some of the left wondered if Wallace would deliver a fair performance given he was the first moderator from Fox News, whose opinion shows generally favor conservative viewpoints.
Fox News host Bret Baier told viewers after the debate that he had "goosebumps" watching Wallace, his co-host for the first Republican presidential primary debate.
"We're all proud of Chris," Baier said.