As a chiropractor (who no longer practices) but has costochondritis, I can tell you that first you need to rule out something more dangerous.
The pain is most likely due to some irritation of the intercostal nerves that innervate the joint, sending excruciating pains around the chest into the back. Sternocostal and costochondral ligaments refer pain from the front of the chest to the mid back.
I used gray's anatomy to refresh my memory and I quote:
"synovial membranes.—there is no synovial membrane between the first costal cartilage and the sternum, as this cartilage is directly continuous with the manubrium. There are two in the articulation of the second costal cartilage and generally one in each of the other joints; but those of the sixth and seventh sternocostal joints are sometimes absent; where an interarticular ligament is present, there are two synovial cavities. After middle life the articular surfaces lose their polish, become roughened, and the synovial membranes apparently disappear. In old age, the cartilages of most of the ribs become continuous with the sternum, and the joint cavities are consequently obliterated."
since there is synovial membranes, one may assume that there is synovial fluid, like in the joints of the fingers and vertebrae. The current hypothesis on joint cracking is that the noise comes from cavitation of the joint, which draws gas out of the synovial fluid and makes a popping sound in the process. You can often cause a popping just by moving/stretching.
I am not too concerned by the pain (because I know where it comes from) and the popping makes a great party trick. You will probably find a lot of misinformation on the subject because most md's have a poor knowledge of physical medicine and many chiropractors are quacks. Try to get yourself to a do or someone who deals with manual medicine. A good chiropractor should be able to figure this out (notice I said a good chiropractor, something of an oxymoron)
the chances are that if you can reproduce or increase the pain by trunk rotation, this is the issue, but still get it checked out to ddx other nasties.
Just to make sure you get it. This post is not medical, chiropractic, naturopathic, homeopathic or psychopathic advice. Just some insight from 4 years of voodoo school