I seriously doubt that the original piece is called Church - it's a gregorian(-esque) chant, and considering that they were wall sung in churches, I doubt that such a generic name would be given to one.
Frankly, I couldn't tell you the name of the chant they used if I tried. They may not even be the same chant (I haven't checked, though). Chants are specifically without rhythm or whatnot, and in Latin. I don't understand spoken latin, let alone the chanted stuff. That makes it more difficult for me, at least, to recognize them.
For another good example of Gregorian chant used in contemporary music, listen to Sadness by Enigma.
BG