The Chainsmokers had an unexpected guest stealing the spotlight during their Austin City Limits performance ... a completely naked man who decided to let it ALL hang out while dancing to their music!

TMZ has obtained video showing the nude festivalgoer busting a move during the electronic duo's set Friday night at Zilker Park in Austin, Texas ... wearing absolutely nothing as he grooves to the music.

The guy is completely in the buff, seemingly without a care in the world as he dances along to the performance. Talk about letting loose!

But apparently, the naked dance party wasn't the only wild part of the night.

The man caused quite the commotion during the show, with festivalgoers claiming he stripped down, smeared mud on himself and became aggressive toward people working near the sound booth.

Witnesses claimed the man threw punches and attempted to damage sound equipment ... with some saying the chaos lasted approximately 10 minutes.

The bizarre spectacle apparently even caught The Chainsmokers' attention ... with Drew Taggart reportedly reacting to the nude fan from the stage.

It's unclear what prompted the man's naked antics or whether police ultimately got involved.