Martin said:
Do you mean that if a joke has obviously being set up and all you need to do is supply the punchline then you should do it? I could not disagree more, that makes it soo dull and obvious.
No, Chekhov's gun is a technique that helps trim the fat from a screenplay. Here's another statement of it that may make that clearer: "If in the first act you have hung a pistol on the wall, then in the following one it should be fired. Otherwise don't put it there."
The Whedon chicken version is just a joke, from a man who has demonstrated that a well-placed chicken on stage can make for a nice piece of whimsey.
*minor spoilers*
Borat uses it mainly for two purposes: first, on the subway in New York, it 'escapes' and he chases it around a bit, adding to the discomfort of a bunch of people who had already shown themselves to be extremely hostile to him even saying "hello" to them. Later, when he seems to have lost everything, he makes the audience gasp as he seems to be about to kill and cook the hen, then lets it go with a parody of a scene familiar from lazy screenwriting, yelling "go" at it, crying, then waving a twig at it - normally used when pushing away someone because he feels hurt, or saving someone with an act of self sacrifice like in a war movie. Borat is doing both. Anyway, I appreciated the chicken-related humour slightly more because it reminded me of the Whedon quote, and I admire him enormously.
*end of spoilers*