I've had 2 herniated discs (specifically c5/6 & c6/7) in the last six years. i have a large chest. is it possible that this is the cause?

I doubt it: There no evidence that people have large chest have more cervical disc problems. There are study to show if a lady have large breasts that could strain her neck and back.

No the disc : Herniations did not cause the large chest nor did the large chest result in the disc herniations but the extra load on the neck could aggravate your symptoms there.