I may be taking the situation in a whole different direction, but consider this:
Is she only saying TO YOUR HORSE, "oh you need a chain!" or did she actually discuss the use of a chain with you?
If she's only saying it to your horse, then maybe it's just like a habit that she says it. And she doesn't actually mean
it. For example, I used to ride this somewhat stubborn POA. If he would do something naughty, his owner/my trainer would sometimes say, "We're going to turn you into some Pony Pepperoni!" Of course, she didn't actually mean we'd ship him off to the slaughterhouse!
If I'm totally off base here, then I'd do as others suggested. Talk to her and let her know you don't want to use a chain. Maybe discuss other options such as a rope halter (even with the little knots on the nose).
Another thing to consider...are you doing groundwork in training for show (Halter)? If so, you probably want to use the same type of equipment for training that you will use in your future shows. If your horse learns to only respond to a chain in training, then you'll have to use one for show as well.