I've read that Charlie had a secret relationship with Lupe for a brief time. I'm not sure if that's true but here's what Lupe said about it in 1929:
Of course, every time you go out with mens in Hollywood, they put it in newspapers. I go once with Charlie Chaplin. Just once-- to the opening of "Lilac Time." They say we are going together. But I like Charlie. I love to listen to him. He has so many brains. He is-- what you say?-- a geen-i-oos. His talk teach me somethings. I want to learn things in this country. Of course, I flirt with him. I flirt with every mans, but that means nothing. (Lupe Velez, "The Love-Life Story of Lupe Velez," Motion Picture, January 1929)