Do Rubber Bands or Chains on Braces Actually Work?

Rubber bands have been helping to correct both Class II and Class III corrections for many dacades.  The underdevelopment of your upper jaw can best be handled with the use of dentofacial orthopedics, in order to expand your upper jaw to eliminate its underdevelopment.  This can be done non surgically even in severe cases, as you can see by looking at my cases on this site or my website.  More traditional orthodontic approaches will use surgery on the more extreme cases, but with good patient cooperation, the surgical approach is not necessary.

The short answer is Yes. Are they enough for all cases? That answer is No.

Will they work for yours? From what you describe, Yes.

You should consider that rubber bands move teeth, not bones. Moving the teeth can improve your profile balance but because they are moving the teeth that sit in the bone, not because they re actually moving the true skeletal foundation. There are only two things that can change your skeletal foundation. 1) surgery 2) lots of very light consistent pressure directly on the bone for years, if you are a nongrowing patient. This last concept allows for the same bony remodeling that occurs as we age but in a directed manner. The second is a hotly debated concept in our field.

If you would like some more upper jaw development, Google reverse pull headgear, it could be another tool in your back pocket to discuss with your ortho.
 

It sounds like the Class III problem is not overly severe and it likely could be corrected using what are termed class III elastics (rubber bands)  in conjunction with braces.  The "chains" referred to are probably elastomeric chains used for space closure in individual dental arches and would not really address the intrer arch discrepancy between upper and lower.  That would be best done by the Class III elastics.  I use the Damon system and I think we do get much better response from the class III elastics than I used to get with the more traditional braces we used before.  Every case of this type needs a very carefully done treatment plan from an experienced orthodontist who will measure and check all of the underlying skeletal structure of the jaws themselves and not just the teeth because this problem is likely related more to the underlying skeletal structure.  I do go to great lengths to avoid jaw surgery whenever possible however in some of the very severe cases nothing else witll do the job properly.