Hey Kahn,
I can't say I particularly know much about your area of focus but, in general, I believe most PhD's are based on an overall thesis statement that is followed throughout the whole piece. I'd recommend maybe doing this other chapter as a separate piece of research instead, it may look quite out of place if it's really different to everything else you're doing. I'd speak to your supervisors about this though as they may say it's acceptable to add it.
A.W