Could chewing on one side of your mouth cause facial asymmetry?

It might: If you chew solely on one side, you are exercising the muscles on that side more than the other side. Just like if you lifted weights with only your right arm, your right arm would become asymmetrical with your left.

Yes but: You wold have to chew on 1side exclusively, which none of us do. We are all primarily right sided, or left sided, chewers, but not exclusively so. We are all, however, slightly asymmetric, and that' sweat makes our faces interesting. If you have concerns, see Oral Surgeon, Orthodontist, or Plastic Surgeon.

Of course: If you chew only on one side of your mouth, the favored side is overused. This results in uneven teeth that twist to one side and muscle hypertrophy resulting in facial asymmetry.

Yes, it's possible: If you only lifted with your right arm, would it become more muscular than your left? Would its bones be stronger, too? Of course. And your face is no different. If you only chew on one side, you are exercising that side much more and so your chewing muscles and bones on that side get bigger. This leads to asymmetry. It can also cause joint (TMJ) problems.

Rarely: First of all the 2 sides of everyone's face are somewhat asymmetric, and have been since birth. An Orthodontist or Orel Surgeon can point out the differences for you. Second, we are all primarily one sided chewers, just like we are either right or left handed. Your body will allow you some leeway as it functions. Most of the time the difference between the 2 sides is very small.