A popular story about the origin of this phrase is that in Las Vegas you could get a nice chicken dinner for less than $2.00. Since winning an average bet would make you over $2.00, the two were equated as being approximately the same value. If you won, you could buy a chicken dinner, and I'm sure that the rhyming factor didn't hurt for people who were rubbing in their win.

Thus the phrase "Winner, winner, chicken dinner" was born.