"Billy, I love your brilliant mind. ... Congratulations! With love and respect always, Angie," the full-page trade ad read.
Thornton joked to Associated Press Television News: "You know, it's funny. ... I've only met Angie Dickinson once."
The 49-year-old "Sling Blade" actor received his star on Hollywood Boulevard as part of the promotion for his new movie, "Friday Night Lights," (search) which is about high school football in Texas.
"You can try to be humble about this kind of thing and say, 'Oh well, it's fine or whatever,'" Thornton told the crowd. "But the fact of the matter is it's a huge honor and I appreciate it so much."