Graham said the clown turned toward their car and slowly waved before running off into the distance.
"I mean, this was somebody putting forth a lot of effort -- and being really weird," Graham told WBBM-TV.
Cemetery officials said there were no reports of vandalism following the sighting, but Graham said she still doesn't like what the person was doing.
"I just think it's creepy and wrong," Graham said.
The encounter was reminiscent of a viral video from last year that depicted a person in a clown costume walking through New York's Greenwood Cemetery holding a bundle of balloons.
Creepy clowns became a nationwide trend during the Halloween season last fall, with pranksters in costumes being caught on video and in photos all across the country.