“Chekhov’s Gun” is a commonly-quoted dramatic principle underscoring the necessity of every element of a narrative story. If a gun is shown in the first act, it must be fired in the third. Elements that do not impact the story — unfired guns — should be removed entirely, so as not to make false promises or clutter the story with unnecessary details. Chekhov’s principle is intrinsically related to foreshadowing, and there are several ways to use it. You can use it well, giving your story the qualities of a fine-tuned machine. You can use it poorly, relying on it as a crutch such that your story loses its natural, organic feeling. Or you can use it like Jean-Luc Godard uses it in Contempt: as a massive fuck you to anyone who dares insist that dutifully following the rules is going to make your story better.
It’s more complicated than that, of course, but the handgun that appears in Contempt is indeed shown several times with great intention. It is never fired, nor is it brandished with the threat of being fired, nor is its owner really the type of man who would ever shoot anyone. That man is Paul Javal (Michel Piccoli), a screenwriter working on a new adaptation of Homer’s The Odyssey while contending with pressure from his American producer Jerry Prokosch (Jack Palance) and navigating marital strife with his spouse Camille (Brigitte Bardot). After a mere glimpse at Paul we understand he is not the type of man to resort to violence, much as we understand after Contempt‘s opening shot that Godard is not the type of director who’d forget that he put a loaded gun in the hand of his hero.
One of the best collections available on the Criterion Channel is one called Film Plays Itself, a self-reflexive assemblage of movies about movies. Here you’ve got your classics, like Sunset Boulevard and 8½. You’ve got your “out-there” stuff, like the experimental Symbiopsychotaxiplasm or Godard’s New-Wave Contempt. And you’ve got some modern triumphs like The Player and 
Motion State Review 