That original song was "When Messiah Comes," and it's really quite terrific. However, it ended up being cut and then replaced by "Anatevka." The reason that such a wonderful song got dropped is -- well, let the lyricist Sheldon Harnick tell you himself, and then sing the song for you.
(What's especially fun about this recording is hearing the very clear pleasure that Mr. Harnick gets from the appreciative reaction of the audience. And a well-deserved reaction it is, too.)