Are you using a western headstall? You could put a leather or chain curb strap on the bit.
A curb strab and a chin strap are two different things. The curb strap goes behind the rein attachment, and it puts pressure up against the lower jaw when the reins are pulled. Used with a leverage type bit.
A chin strap is used with a snaffle bridle, is attached in front of the rein attachement, and applies no pressure against the jaw when the reins are pulled. It only disallows the bit to be pulled sideways through the horse's mouth when using lateral pull.