Is there a chicken in your garden?

Last night Chihiro, Liz, Katie and I went out to eat at this great Italian restaurant with an all-you-can-eat bread bar. While we were there a conversation started about the Japanese phrase, "niwa niwa niwa niwa tori ga iru." This is a play on words and the word niwa can mean "garden" "two chickens" "to be"... So the phrase translates to "there are two chickens in the garden." And it sounds fun when you say it. However, in our discussion, Katie was a little confused about the garden, and who's it was and if there was a Mr. Niwa in the story. Here is our conversation