"Winner winner chicken dinner"

What's the proper context to use this phrase? And who would usually say something like this? Sounds very childish.

You would use this when someone won something, but it's quite colloquial. The "chicken dinner" part is just a nonsense rhyme, in the same class as "easy-peasy" (including its citrus and racist variations).

This is usually heard in casinos. The croupier or dealer calls it out when someone wins (obviously). It comes (allegedly) from the days when a chicken dinner cost about as much as a minimum bet at one of the table games ($2). So winning such a bet was enough for a meal. The rhyme made it stick, of course.

I'm quite sure I heard it in a movie, maybe "21" in the underground casino scenes. I don't think it's used in real life though.