It's one of those famous Hollywood fights: Bill Murray vs. Chevy Chase. Although it was more than 30 years ago, it's still a topic of curiosity for fans of the two actors and "Saturday Night Live."

When Murray stopped by "The Late Show" on Thursday, Letterman took the opportunity to ask his frequent guest about the confrontation, which according to both Murray and Chase has long since been put to rest.

In an explanation somewhat akin to Powers Boothe's in "Red Dawn" — "Two toughest kids on the block... Sooner or later, they're gonna fight..." — Murray gave Letterman some insight into the altercation backstage at "SNL" that would eventually became the topic of so much speculation over the years.

Watch the clip above and let us know whether you're on Team Bill or Team Chevy.

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  • Bill Murray & 'Moonrise' Cast

    US actor Jason Schwartzman, US actor Bruce Willis, US director Wes Anderson, US actor Edward Norton, British actress Tilda Swinton and US actor Bill Murray pose during the photocall of 'Moonrise Kingdom' at the 65th Cannes film festival on May 16, 2012 in Cannes. (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray & Bruce Willis

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray & Bruce Willis

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray, Tilda Swinton & Ed Norton

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray & Tilda Swinton

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • US actor Bill Murray and British actress

    US actor Bill Murray and British actress Tilda Swinton pose during the photocall of 'Moonrise Kingdom' at the 65th Cannes film festival on May 16, 2012 in Cannes. AFP PHOTO / ALBERTO PIZZOLI (Photo credit should read ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray & Tilda Swinton

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray

    (VALERY HACHE/AFP/GettyImages)

  • Bill Murray & Bruce Willis

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray & Bruce Willis

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • Bill Murray

    (ALBERTO PIZZOLI/AFP/GettyImages)

  • US director Wes Anderson (L), US actor B

    US director Wes Anderson (L), US actor Bruce Willis and US actor Bill Murray (R) arrive for the screening of 'Moonrise Kingdom' and the opening ceremony of the 65th Cannes film festival on May 16, 2012 in Cannes. AFP PHOTO / ANNE-CHRISTINE POUJOULAT (Photo credit should read ANNE-CHRISTINE POUJOULAT/AFP/GettyImages)

  • US actor Bill Murray arrives for the scr

    US actor Bill Murray arrives for the screening of 'Moonrise Kingdom' and the opening ceremony of the 65th Cannes film festival on May 16, 2012 in Cannes. AFP PHOTO / ALBERTO PIZZOLI (Photo credit should read ALBERTO PIZZOLI/AFP/GettyImages)