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"Lorne Michaels called me and he said, 'You have a lot in common with Chris Farley. Would you please spend time with him?'" Arnold told Stern, 67.
He went on to become Farley's sobriety sponsor.
"You know, he wanted to be sober," Arnold said of Farley, who died in 1997 of a drug overdose. "And I think Lorne really worried about that. So I was his sponsor for a few years."
Describing their relationship as "very close," Arnold said the two comedians bonded over growing up in the Midwest and football. "He liked to have fun," Arnold said of Farley, "he had too much fun. [I was] very sad when he died."
Elsewhere in the interview, Arnold opened up about one of his favorite memories of Farley.
When Stern asked what Arnold's bachelor party - thrown by Farley - was like, the former Roseanne star said, "we did it at Scores," a famous strip club in New York City.
"What happened was, all the guys, David Spade was in the wedding, there was a lot of guys ... and Farley disappeared," Arnold recalled. "And then came on stage, naked."
"And then they ended up kicking everybody out, I mean, because he was a big guy. He did not mind being naked," Arnold said.
"Chris Farley gets on the stripper stage and removes all his clothing and starts dancing?" Stern asked, as Arnold shook his head "yes" in confirmation. "I mean, what a commitment to comedy."
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Arnold then recalled one of Farley's most iconic SNL sketches: the Chippendales audition alongside Patrick Swayze. Arnold revealed that Farley had been hesitant to do the sketch, but he encouraged his friend to "go for it."
"He called me that week," Arnold remembered, "and he said, 'I am so embarrassed, they wrote me this thing, and [it's embarrassing] 'cause I'll be the fat guy next to Patrick Swayze. What do you think?'"
Arnold said he told Farley: "If you can be the funniest fat guy ever doing this thing, then you should do it. And you should really go for it."
"He was naked a lot," Arnold added. "There's no shame in his game."
If you or someone you know is struggling with addiction, please contact the SAMHSA substance abuse helpline at 1-800-662-HELP.