Charlie Chaplin was doing a clear parody of Hitler in "The Great Dictator," and that movie well have been the first Hollywood film in production mocking him. However, because of the relative quickness of making a short, another comedian can claim the honor of being the first parody of Hitler *released* to mainstream American audiences. What comedian portrayed a (nameless, but clearly Hitlerish) dictator in "You Nazty Spy?"
Moe Howard, Moses Horowitz