The Neurosis song Stripped has a chant part in it. Just that one song though.
It’s not strictly what you’re looking for, but if you “like the juxtaposition of heavy metal with symphonic and other non-traditional instruments, as well as non-traditional vocals” I have to recommend Devil Doll to you. Try to get your hands on either Dies Irae or The Sacrilege Of Fatal Arms.
Industrial Monk didn’t quite do it for me, but In Extremo is pretty sweet–thanks for pointing them out.
Not chants, but in the rock-with-traditional-instruments genre that ultrafilter mentioned, some of my faves are:
Ashley MacIsaac’s celtic fiddle-rock, with some gaelic R&B, and bagpipe rock thrown in as well.
Blind Guardian - esquisitely overproduced synphonic metal. My favorite is, Nightfall on Middle Earth, the Silmarillion as metal-rock opera. (A little bit Queen, a little bit metallica, a dash of Iron Maiden, and some flutes and such)
Jethro Tull, as mentioned before. Rock with a flute. My favorite is Songs from the Wood. Very folksy and pagan sounding.
Apocalyptica, a hard-rock cello quartet. Started as a metallica cover band, but branched into orginal work.
There’s a quite good mp3 of a techno version of Carmina Burana by Apotheosis floating around the net.
Well, it’s not strictly what I was looking for, but I heard the first track off Ulver’s Bergtatt, and they had some nice vocal harmonies going with some decent metal. I’ll definitely be looking into it, and I thought some of you might be interested.
Probably not what you are looking for since they are very relaxed, but here on Amazon:
50 Gregorian chants remixed for $0.99
Haven’t had a chance to listen to them all, there might be SOMETHING for you in there!
Sanctified by Nine Inch Nails, from the Pretty Hate Machine album.
That was the song that immediately came to mind when I saw the thread title.
Aaaand now it’s stuck in my head. At least it blew the other earworm out of my head, which was Wanted Dead or Alive by Bon Jovi. 
Neither metal nor Gregorian chant, but I always like to plug The Rap Canterbury Tales in these kinds of threads.
yeah that was the full mass. especially interesting if you were familiar with the mass.
Please keep in mind that the first 24 posts in this thread are 10 years old.
In case anyone is still interested in zombie Gregorian rock chant, check out the band “Gregorian.” They do Gregorian-chant versions of modern pop and rock songs. I have their CD “The Dark Side” and like it a lot.