Tolkien wrote a number of important things in their "original" fictional language -- the language of Mordor for the inscription inside the One Ring, the language of the elves for quotations from their history and poetry, in a few places he even used the language of the dwarves. When necessary, he supplied a translation into English (couched as translating into the "common speech" for one of the hobbits, usually). In several places he used an elvish word, then explained (character to character) what he meant. For instance, lembas, elvish waybread -- the explanation of what it was accompanied warning Pippin that, in one bite, he'd eaten enough of what he thought was ordinary cram, what we'd call hardtack, to support a long, hard day's march.
His way still works very well, and doesn't really require you have a complete language as background -- unless you have enough examples for too-complete fans to decide you've been inconsistent, there's really no need for it. Tolkien did it as a hobby, because by profession he was a philologist -- he studied the structure and evolution of real languages, and taught the same subject at a university.
However: whether to write something as substantial as a chant in its original, and whether to translate it immediately (as opposed to, say, in an appendix) ought to depend more on what character's POV you're writing in. If you're writing from POV of a native speaker of the chant's tongue, I'd write it in English -- because the speaker will understand it without effort or thought. If the POV character understands the language as a "second" tongue, you might supply a basic translation -- perhaps one character summarizing for another. If the POV is from a character to whom the language is gibberish, you'd want to reproduce it as heard, or even just allude to it as unintelligible (speech you don't understand is terribly hard to remember, compared to speech that makes sense to you).