Could be a tension thing. I have some chenille in my stash, but haven't used it yet. When I swatched with it, I noticed that a looser gauge made it lay flatter when I used ordinary stockinette. (Makes sense, right?) If you don't mind it being less dense, you could try that. I don't think chenille is supposed to be the easiest type of yarn to work with -- there is something called "worming"
that it's prone to, when the yarn curls up on itself.