What Book Of The Bible Tells The History Of How Israel Became God's Special People?

That would be Exodus, but remember that this book was written by those people, so we only have their word for it, and they just might be ever so slightly biased! Nothing special about them, so far as I can see.

Actually, Exodus is only an extension of the story, an extension of how God seemingly relates to his special people. Genesis actually gives the full reasons with the story of Abram or Abraham. He is the initial patriarch of the nation. His story starts in chapters 11 and 12 of Genesis and the stories of his descendants winds its way through that book.