Can my 32H breasts be the cause of chronic, but not severe, low back pain? I'm 5'3" and 135lbs.

Larger breasts may be involved in causing lower back pain. It is quite possible. A reduction may help with the lower back pain, but an evaluation by a back specialist may be beneficial as well.

Lower back pain can have many contributing factors.  Large breasts can be one of these factors, but perhaps not the only one.  A thorough history of your problem and physical exam performed by your primary care physician is the appropriate first avenue of treatment.  Your physician may recommend NSAIDS, Physical Therapy, and some diagnostic tests (Xrays) to help sort out the problem. Age appropriate breast imaging would also be recommended.  In terms of breast reduction surgery...If your musculoskeletal problems are ultimately linked to your breast hypertrophy, there is plenty of evidence that indicates that breast reductions are safe, reproducible and helpful. A board certified plastic surgeon would be your best resource to discover if a breast reduction is right for you.