You know, the way it's mentioned here, it makes Chekhov's gun sound like a trite, hackneyed formula. It's actually a rule of dramatic writing. You can't have someone pull a gun out of a drawer in Act 3 if you haven't alluded to the gun's presence already (and I would argue you can't just allude; the audience must be made aware there's a gun there)--and I say "you can't" not because you can't, but because the audience will feel cheated. Similarly, you don't place a gun somewhere on the set/in the story without intending to use it later, for similar reasons.
I had to look this one up. From Wikipedia: "Chekhov's gun is the literary technique whereby an element is introduced early in the story, but whose significance does not become clear until later on. For example, a character may find a mysterious object that eventually becomes crucial to the plot, but at the time of finding the object, does not seem to be important."