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Chimaev, 26, made his UFC debut back in July against John Phillips and currently holds an unblemished MMA record of 9-0, with six victories coming by way of knockout.
The Russian-born Swedish fighter, who also defeated Rhys McKee in July, once again put the MMA world on notice with his performance at UFC Vegas 11 on Saturday.
White, 51, was blown away by Chimaev's performance and said the "kid is absolutely special and I've never seen anything like it."
The UFC chief told Megan Olivi during the UFC Vegas 11 post-show: "One punch. Seventeen seconds. This kid is special. He's different than any fighter I've ever seen.
"I've been in the business for a very long time, I've seen a lot of greats come and go; this kid is absolutely special and I've never seen anything like it."
White continued his praise of the undefeated UFC fighter as he once again reiterated that Chimaev is "one of the most special fighters I've ever seen."
He explained: "The guy's special. I've been in this game my whole life, I've never seen anything like him. He's special, he's different and he wants to fight again.
"I've never been in a position where I'm like, 'Who's next? How do we get him a fight? How do we get him over here, how do we get him over there? How do we do this, how do we do that?'
"It's fun and I like it and I think when you're a fight fan a guy like this is who you love to watch and follow and hate and whatever it might be.
"This guy is one of the most special fighters I've ever seen, if not the most special guy that I've ever come across."
Chimaev has previously voiced his desire to set up super-fights with the likes of Conor McGregor, Nick and Nate Diaz and Demian Maia.
White has revealed that the 26-year-old could face another opponent before UFC book a fight with him against Maia.
"That's what everybody is saying," the UFC president said.
"This guy is special, man. It's true. [...] I don't know what I do with him yet. He might fight before Maia and fight Maia, too. Maia's not going to be ready in time for this kid."
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