Will Chin Implant Improve Facial Symmetry?

Chin implants are great for improving the projection of your chin as well as correcting any asymmetries. For you, I would most likely use a Medpor implant as it can be carved out during the operation to provide you the symmetry that you're looking for. It's an outpatient procedure and very well tolerated. Good luck!

It is possible to customize and implant to compensate for facial asymmetry. It is easier to place a mandibular angle implant on one side than it is to correct an asymmetrical chin. However, both are possible.
Facial asymmetry is a natural thing that can, in many cases, add interest to the face that equates to beauty. If you know how to use photoshop, then you should take some models and make a whole face from either half of their face. The perfectly symmetric face that you construct is typically less attractive than the original asymmetric one. I make my residents do this exercise as part of their training.
That being said, if your asymmetry is an issue, then it is possible to correct or minimize the asymmetry you describe.

While a chin implant can make a chin project more in an anterior projection, it usally achieves this wth a symmetric implant. Placement of a symmetric implant over an asymmetric surface as your describe may do little to correct the problem. In fact it could make it more noticeable. As stated elsewhere here, fillers may be good for mild corrections.