Scott Weiner, 28, co-owner of The Fifty/50 sports bar, said the magazine, which featured Phyllis Babila on the cover, was taken from a glass frame in a bathroom while a 1972 Playboy and a 1973 issue were left behind in the same frame, the Chicago Tribune reported Thursday.
Weiner said he initially suspected a jealous relative of Babila was behind the theft.
"That's the only thing I would think of," he said. "(She is) somebody's relative. They saw their mom up there and thought, 'I'm taking that down.'"
However, Babila said she does not have any children or ex-husbands in the Chicago area. She said she was "impressed" with the thief's effort.
Weiner said he and co-owner Greg Mohr are offering a $100 gift certificate to The Fifty/50 and a May 2009 Playboy autographed by model Crystal McCahill for the safe return of the missing magazine.
"The Playboys have always been kind of a sacred thing," Weiner said. "No one's really messed with them before."